Solve for x: $$\log_2(x^3)-3=2\log_2 x$$
I tried solving this by converting everything to base 2:
$$\log_2(x^3)-\log_2(8)=2\log_2 x$$
Then using the log rules to combine the LHS:
$$\log(\frac{x^3}{8})=2\log_2 x$$
But I'm stuck on what to do next.

Question

anonymous · Answer

$$\large \log_2(x^3)-3=2\log_2 x$$

is it this?

anonymous · Answer

Yep.

anonymous · Answer

get the logs on one side of the equal sign and put that three by itself on the other...
what do you have?

anonymous · Answer

oops.. you actually showed your work but my computer is not showing it properly.. can you show me where you got stuck?

anonymous · Answer

One second, I didn't actually put 3 on the other side by itself and instead turned it into a log. Give me a second to see what I get.

anonymous · Answer

Hey thanks! I got it! By putting the x's on one side alone, I was able to simplify the x^3 and x^2 to x and then it was very simple to solve by then. Thanks!

anonymous · Answer

yw.. :)