A logarithm is another way of thinking about exponents.

We know that 2 raised to the 4th power is 16. Now imagine if someone asked you what “2 raised to which power equals 16?” the answer would be 4. This is shown by the log equation log2(16)=4 it would be read as (log base 2 of 16 is 4).

 

24=16

both equations describe the same relationship .

 

The difference is that while the exponential form isolates the power, 16, the logarithmic form isolates the exponent, 4

 

 

The form for solving these is

a⋅b^​​=c

Solve 5⋅2^=240

To solve for x, we must first isolate the exponential part. To do this, divide both sides by 5 as shown below. We do not multiply the 5 and the 2 as this goes against the order of operations.

 

5⋅2x=240​​​​​

 

2​x​​​​​​=​=48​​

Now we can solve by converting it into log form which would be 

 

When rewriting an exponential equation in log form or a log equation in exponential form, it is helpful to remember that the base of the logarithm is the same as the base of the exponent.

 

 

 

 

 

 

 

The common logarithm is a logarithm whose base is 10 .When writing these logarithms mathematically, we know the base. It is understood to be 10.

The natural logarithm is a logarithm whose base is the number e. Instead of writing the base as e, we show the logarithm with LN natural log.

loge(x)=ln(x)