Question

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

Answer 1

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.

Answer 2

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

Answer 3

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

Answer 4

that second one

Answer 5

idk how to key in the bases

Answer 6

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.

Answer 7

thank you... i really appreciate it

Answer 8

Happy to help!