# Thread: Logarithm question [won't take two seconds!]

1. ## Logarithm question [won't take two seconds!]

The question asks to solve

$\displaystyle log_a (3x + 4) - log_a x = 3 log_a 2$

I have got to

$\displaystyle log_a \frac{3x + 4}{x} = log_a 8$

But I'm not sure if this is the correct method or what to do after this to solve it.

2. Hi

I would advise first to find the domain of $\displaystyle log_a (3x + 4) - log_a x = 3 log_a 2$

$\displaystyle 3x + 4 > 0$ and $\displaystyle x > 0$ therefore $\displaystyle x > 0$

Then OK for your method which leads to $\displaystyle \frac{3x + 4}{x} = 8$

Solve for x and do not forget to check if $\displaystyle x > 0$

3. Originally Posted by running-gag
Hi

I would advise first to find the domain of $\displaystyle log_a (3x + 4) - log_a x = 3 log_a 2$

$\displaystyle 3x + 4 > 0$ and $\displaystyle x > 0$ therefore $\displaystyle x > 0$

Then OK for your method which leads to $\displaystyle \frac{3x + 4}{x} = 8$

Solve for x and do not forget to check if $\displaystyle x > 0$
I got 0.8 for x because I realized just now the method I needed! Thanks for helping.

4. Originally Posted by db5vry
I got 0.8 for x because I realized just now the method I needed! Thanks for helping.
That's it