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ln e^ 81 is always 81 because ln means logbase e, so e^x = e^81 (when you convert it back to exponential form) and since the bases are both e then the exponents must be equal!!!!

so ln of e^any power is that power!!!!!

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log 3 with base 9 is equal to 9^x=3.
(9^x=3) is equal to 3^2x=3^1
Since bases are now equal, the two exponents are equal.
3^2x=3^1 is now 2x=1
Divide the one by the two, and you get 1/2=x

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basically if you solve the logarithm then youll get it right. knw how tok solve logarithms and youll get it right

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Our equation is: 3 log 2 + log 9
We need to make a single log function from this equation.

1.) 3 log 2 is the another way to write the log of log 2³. 2³ is 8, therefore the first log is changed to log 8. (Power Property)

2.) Since the Product Property tells us that a log plus a log is equal to a log multiplied, we multiply our two numbers, 8 and 9, and we're left with log 72.

Since we're only asked to make a single log function, our answer is log 72

we did it

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2^5x=*8
write in exponential form
2^5x=2^3
set exponent to equal
5x=3
divide by 5
3/5 =

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Expand the logarithm. Simplify if possible.

You will have to use the Quotient Property:
logb m/n = logb m - logb n

My problem was log6 r/s
By using the quotient property you should get
log6 r - log6 s

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Suppose that a new employee starts working at

​$7.98

per hour and receives a

44​%

raise each year. After time​ t, in​ years, his hourly wage is

given

by the equation

y=$7.98(1.04)^t.

Find the amount of time after which he will be earning​$10.00 per hour.

First, substitute 10 for y as 10=y and create the equation :
10=$7.98(1.04)^t

To solve for t, start by dividing 7.98 from both sides of the equation to get:

10/7.98= 1.04^t

To find t, you need to take the common log of the equation using the logarithmic properties.
log(10/7.98)=t log1.04.

Finally, divide by log1.04 to isolate t.:
t=log(10/7.98)/log 1.04.

Simplifying the equation via calculator you should get 9.1 as the answer.

Therefore, the hourly wage for the employee will be $10 after 9.1 years.

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To expand a logarithm, use the product property of logarithms to write it as a sum of logarithms

so, log ₂32auc becomes:

log ₂32auc=log ₂ 32+log ₂a+log ₂u+log ₂c

Now simplify log ₂32  and add it to the beginning of the sums

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Q: Solve the equation
log 2x + log x=10
Apply the product property of logarithms to simplify the left side
log (2x^2) x=10
Write in exponential form
2x^2 = 10^10
Divide and square the right side by the left

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First the rewrite the equation in logarithmic form. To do that you would want to remove the e which the inverse of e is natural log or ln so to remove the e you want to do the natural log of the other side of the equation. After you remove the e and bring down the exponents. Then find the natural log of the other side of the equation. If the variable in the exponent is attached to a number divide the other side of the equation by the number attached to x.
These steps would look
like this:
e^(number)x = number
(number)x = ln number
x = ln number/number
x = number

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f(x)=ab x-h+k
If the 'b' of the equation is >1 the graph has exponential growth.

If the 'b' of the equation is 0<b<1 (between 0 and 1) the graph has exponential decay.

the y-intercept is 'a'. (when x=0)

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y=log_7 x

Here is the graph.                                To solve it on Desmos, you would enter y=log_7 x. The _ is a subscript that can be found at the top of your keyboard.

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Make a table of the values by plugging in numbers for x. After that, you just match up the values on the answer choices until you find the right one.

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Q:  How does an earthquake of magnitude 7.8 compare in intensity with an earthquake of magnitude of 3.7 on the Richter​ scale?
A: 1) First you subtract 7.8 - 3.7 = 4.1
2) Then you put 4.1 as exponet for 10^4.1 = 12,589.25 and you round to the nearest whole number and you'll get the answer which is 12,589.

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Q: log_5 125
A: take the function and equal it to y, then follow the steps to change log form into exponential form  1. convert to exponential form
2. make the same base
3.solve the exponent
so in the case of the problem above
this is how you solve it :)

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Q: Compare a graph to it's parent function.

y=logbase(5) x + 3 for example
All of the log functions have the same general shape, no matter what the base is.  They start out small at the bottom of the y axis, increase to the point (1,0), then flatten out as they approach the horizontal asymptote.  In this example, that graph is shifted up 3 units because of the +3 on the end.  If the +3 was in the ( ) like log(x+3) that would shift it left 3 units. IF you want to graph a log in desmos with a different base, click the keyboard, then FUNCTIONS, then MISC to find the log with a different base than the common log of 10

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Q: Solve for x.
3^2x = 15
A:1.) Always check to see if your problem can have a common base; in this case the equation can have a common base of log. Take the log of each side.
log 3^2x = log 15
2.) because log 3^2x has an exponent, use the power property to move the 2x in front of log 3.
2x log 3 = log 15
3.) divide both sides by log 3 first.
2x log 3 = log 15                log 15
-------------    -----------  =  2x = ----------
log 3           log 3                 log 3

4.) then divide by 2.
2x = log 15               log 15
----    ----------  =   x  =  -----------
2          2                     2 log 3
5.)  solve for x by dividing the log of 15 (1.17609125906) by 2 log 3
(get the log of 3( 0.47712125472) and multiply it by two( 0.778151250384 ))) leaving you with:

1.17609125906

---------------------------- = 1.23248676
0.778151250384

6.) Approximate.
x = 1.2

7.) Celebrate your epic gamer win

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Principal, $5000;
Annual interest rate, 5.4%;
Time, 2 years

1. Use the continuously compound interest A= (P)(e^rt) and plug in principal for P,
annual interest rate for r,
and time for t

A= 5000e^(0.054)(2)

2. Simplify the exponents

A=5000e^0.108

3. Use a calculator to plug in
e to the power of 0.108

A=(5000)(1.11405)

4. Multiply

A= $5570.25

And that is the balance after 2 years :)

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Q: Solve:
log(21 - 4x) = 0

Step 1:
Remove log from the equation by putting it in exponent form.
(21 - 4x) = 10^0

Step 2: Since anything raised to the power of 0 is one,
(21 - 4x) = 1

Step 3: Combine like terms; subtract 21 from both sides
(21 - 4x) = 1
-21            -21
-4x = -20
Step 4: Divide to get x by itself
-4x = -20
/-4    /-4
x = 5
A:
!!!!!x = 5!!!!!
This is Pate Street

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Q: Find the growth or decay factor, given a rate or change
A: remember that in the formula for amounts it's (1+r) or 1 + the rate. That entire number is considered the growth factor so if my rate is say 80%, then that's .80 as a decimal, so (1+.8) is a 1.8 growth factor. if my rate is over 100%, say 400%, then that's 4.0 as a decimal or (1+4.0) which is a growth factor of 5 {think of the 1 as 100%}

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Suppose we wanted to write the expression...
ln 2 + ln 6
...as a single natural logarithm.

1. First, we should look at the integers present, which are "2" and "6".

2. Now, we need decide which property is best suited for this kind of expression. The Product Property (go revisit your notes or look it up to see it) is best suited for this equation.

3. Lastly, we would plug in our numbers to the Product Property, which should make the expression end up like this: ln 2 + ln 6 = ln (2*6)

4. Our outcome should be:
ln 12
Which would be your answer.

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choose the correct graph: y=-2^x
This one is really easy. Two of the four answers are not even options for real because one is just a straight line or a linear line and the other is a quadratic, so both of those are out of the picture. Then you have to notice that the beginning number is a negative two, so you know the graph must be a descending graph.

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1)Tn order to find the log form, you must find the format of logB^A = X of 343= 7^3.

2)One way of looking at it is with B^X= A and Needs to go to to Logb^a=x

3)in the problem the B is 7, the A is 343, and the X is 3. That written out is Log7^343 = 3.

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y=-1/6 * 8 x

1) If Y= a * b(x-h) + k, determine if the graph is stretched or compressed using the a factor
- stretched : |a| > 1
- compressed : |a| < 1
|a| = 1/6 --> the graph is
compressed by a factor of 1/6

2) Determine if a is negative,
if it is the graph is reflected across the x- axis
a is negative --> the graph is
reflected across the x-axis

3) determine if the graph was translated by checking for h and k values.
there are no h or k values

--> the graph was not translated.

4) CELEBRATE (most important step)
WOOT WOOT *confetti*

    ( \__//)
    .'     )
 __/b d  .  )
(_Y_`,     .) LLAMA!
 `--'-,-'  ) (important)
      (.  )
      (   )
     (   )
    ( . )

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e^5x=18
1. Rearrange the problem into a natural logarithm.
ln18=5x
2. Divide by 5.
3. put ln18/5 into the calculator.
4. The answer is 0.5781 (Round to the 4th decimal place)

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Use the properties of logarithms to evaluate the expression
1. use power property of logarithms on the second term.
log_7  343 --2 log_7 7
= log_7 343 - log_7 49
2. use quotient property of logarithms and simplify
log_7  343.49
=log_7  7
3. lastly simplify log_7   7
=log_7 7^1
which equals 1

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2ln8 Write the expression as a single natural Logarithm.
Solve:
Apply the power property to write the expression as a single logarithm.     ln8^2
Simplify the expression. ln64

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The amount of​ carbon-14 in an object is given by y=a*e^-0.00012t where a is the amount of​ carbon-14 originally in the​ object, and t is the age of the object in years. A fossil bone contains 16​% of its original​ carbon-14. What is the approximate age of the​ bone?
In the given equation, we know that y is the amount of carbon-14 after t years. The problem tells us that "

A fossil bone contains 16​% of its original​ carbon-14." Using this information, we can assign y=0.16a, and plug this into the equation for the amount of carbon-14 in an object. Doing this, we get 0.16a=a*e^-0.00012t. Now, we solve for t, time.

Divide by a: 0.16=e^-0.00012t

Rewrite as a natural logarithm: ln(0.16)=-0.00012t

Evaluate the natural logarithm using a calculator: -1.83258=-0.00012t

Divide both sides by -0.00012: 15271.5=t

Round to the nearest integer as specified by the problem: 15272

*This problem can be solved with any amount of carbon-14*

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1. Use the Power Property to rewrite the first logarithm "x ln m" as "ln m^x"
2. Use the Product Property to combine the two natural logarithms
------ ln m^x + ln n = ln m^xn -------
if MathXL generated the logs
8 ln m + ln n, the final answer would be ln m^8n

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A population of 110,000 grows %5 per year for 15 years. How much will the population be after 15 years?
Solve like this:
Here is the formula...
f(x)=p(1+r)^t
Put the population in first, the rate of increase in parentheses, and the time as your exponent (x). It should look like this...
f(x)=110,000(1.05)^15
You can use desmos or your calculator and your rounded answer should look like this:
228682 people after 15 years