solve the equation.
(1/3)log2^(x+6)=log8^(3x)
the answer is 3.
show me how and why...

Question

somethingawesome · Answer

It's not true as written, are you sure you copied the question correctly? If we plug in x = 3, we get
3 log(2) = 27 log(2),
which is false.

anonymous · Answer

well unless i got the answer wrong from my teacher... my answer choices are 
a) ø
b) 3, 0
c) 3
d) 9

somethingawesome · Answer

Well, maybe I'm misinterpreting it. Do you mean:
$$\log(2^{x+6})$$ or $$\log_2(x+6)$$

anonymous · Answer

that second one

anonymous · Answer

idk how to key in the bases

somethingawesome · Answer

Ok, that's what my problem was :)  it might be clearer to write log_2(x+6).

We need to change the base of one of them, and that formula is $$\log_b(x) = \frac{\log_k(x)}{\log_k(b)}$$ so $$\log_8(x) = \frac{\log_2(x)}{\log_2(8)} = (1/3) \log_2(x)$$ since log_2(8) = 3. Then we now have
(1/3) log_2(x+6) = (1/3) log_2(3x)
by substituting what we just found. Cancel things out and we have to compare the insides, since they have the same base.
x+6 = 3x
has the solution x=3.

anonymous · Answer

thank you... i really appreciate it

somethingawesome · Answer

Happy to help!