# Solving basic exponential equation with logs

I am having trouble with this grade 12 pre-calc question that I am sure will be elementary to most of you. I understand most of it but I do not understand one of the steps.

These are the steps in my answer-key:

$4 = log_2x+log_2(x+6)$

$4 = log_2(x^2+6x)$

$2^4 = x^2+6x$

What happens to 4 to become $2^4$? Thanks!

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Hint: how do you get rid of the $log_2$ on the RHS? Look at laws of logs. –  Amzoti Apr 18 '13 at 4:57

Recall that $$\log_a(b) = y \iff b = a^y$$ In your case, we have $$\log_2(x^2+6x) = 4 \iff x^2+6x = 2^4$$