Example

Let’s now solve a few problems.

Solve 4x = 16

Let’s start by taking the log of each side:

log 4x = log 16

Now let’s use one of the log rules I presented before to rewrite the problem as follows:

so we get
  x log 4 = log 16

Now lets divide both sides by log 4

x = (log 16) / (log 4)

This equals = 2

Example

Now let’s try one more:

Solve for the x in the following: 3ln3 + ln(x - 1) = ln 36

Here are the steps:

First let’s simplify 3ln3 using our rules such that you get:

ln27 + ln(x -1) = ln 36

This can further be simplified to the following:

Ln27(x-1) = ln 36

Now we can divide by the natural log on each side to get the following, which is a simple algebra equation.

27(x-1) = 36

Now divide each side by 27 than add one to each side and you will see that:

X = 2.333