# How do you condense log (3x+1)=2?

Jan 13, 2016

$x = 33$

#### Explanation:

This can be rewritten as

${\log}_{10} \left(3 x + 1\right) = 2$

To undo the logarithm with base $10$, exponentiate both sides with a base of $10$.

color(red)(cancel(color(black)(10^(log_10))))""^((3x+1))=10^2

$3 x + 1 = 100$

$3 x = 99$

$x = 33$

Jan 13, 2016

Just another way of writing exactly the same thing!

$x = \frac{99}{3} = 33$

#### Explanation:

Given: ${\log}_{10} \left(3 x + 1\right) = 2$

2 is the index that 10 has to be raised to give 3x+1. So we have:

${10}^{2} = 3 x + 1$

$100 = 3 x + 1$

$3 x = 99$

$x = \frac{99}{3} = 33$