Question

41. Find all solutions to the following equations. Remember to check for extraneous solutions.

1. log2(3x + 7) = 4

Answer 1

Ans.

X=3

Explanation:

Ok, there are several ways to solve this, I chose the one that can be more visual friendly to you.

SInce the log are based 2, we are going to be using this base on both sides of the equation, so, let Y = (3X+7).

`Log_(2) (Y)=4`

`2^{Log_(2) (Y)} =2^(4)`

This means.

`Y=2^(4)`

Since Y = (3X+7)

`3X+7=2^(4)`

`3X=16-7`

`3X=9`

`X=(9)/(3)`

Therefore X=3

Best of luck.