Question

Which of the following shows the true solution to the logarithmic equation 3log2(2x)=3

Answer 1

3log2(2x)=3
log(2(2x))^3=log1000
8(8x^3)=1000
x=2.5

Answer 2

x=1

Explanation:

`3log_2(2x)= 3`

We need to solve for x

First we divide both sides by 3

`log_2(2x)= 1`

We convert log form into exponential form

If
`log_b(x)= a` then b^a = x

`log_2(2x)= 1`

2^1 = 2x

2=2x

divide by 2 on both sides

x=1

we need to verify our solution

`3log_2(2x)= 3`

`3log_2(2(1))= 3`

3=3 --> true, so x=1 is our solution