Question

HELP !! PLEASE!!
Solve
Log(little 8)2=x without calculator
PLEASE

Answer 1

\[\log_{8} 2=x\]

Answer 2

\[\large \log_a (n) = y \implies a^y = x\]\[a=8~,~ 2=n~,~ x=y\]

Answer 3

So you'll have \[\large 8^x = 2\]\[\large 8= 2^3\]\[\large (2^3)^x=2\]\[\large 2^{3x}=2\]Take \(\log_2\) of each side to get rid of the base so you can solve for the exponents.\[\log_2(2^{3x})= \log_2(2)\]Remember, \(\log_a (a) = 1\)

Answer 4

okay so it gives you \[\log4^{3x}=\log4\]

Answer 5

are we just solving for x like find the value that makes \[\log_82=x\] true?

Answer 6

that's 3.

2^x = 8

Answer 7

so what x value produces 8 on the right? Well if I take the base 2 to the 3rd power I will have 2 x 2 x 2 = 8 or 2^3=8/ That's about it.

Answer 8

Also: \[
\log_a(b) = \frac{\log_b(b)}{\log_b(a)} = \frac{1}{\log_b(a)}
\]Interesting.

Answer 9

So \[
\log_8(2) = \frac1{\log_2(8)} = \frac1{\log_2(2^3)} =\frac1{3}
\]

Answer 10

Smarties.

Answer 11

so the answer is 1/3 ? sorry for late reply