Given the exponential equation 2x = 8, what is the logarithmic form of the equation in base 10?

Question

anonymous · Answer

WAIT actually I might have got it, so could someone just check my answer?

anonymous · Answer

Is it log(10) 8 / log(10) 2????

solomonzelman · Answer

$\normalsize\color{blue}{ 2^x=8}$

The relation is     $\normalsize\color{black}{ A^B=C~~~~~~~~→~~~~~~\log_AC=B}$

solomonzelman · Answer

$\normalsize\color{blue}{ 2^x=8~~~~~~~→~~~~~?}$     you tell me

anonymous · Answer

log(2)8 = x

solomonzelman · Answer

Yes, but you need in base of 10, so apply,   $\normalsize\color{blue}{ \log_DC=\huge\frac{Log_{10}C}{Log_{10}D}}$

anonymous · Answer

exactly, couldn't you apply base of 10 from the beginning?

solomonzelman · Answer

well, not really, because of the relation, you at first need to have the base 2.

anonymous · Answer

okay, so from there how do you go about switching it into base of 10?

anonymous · Answer

@SolomonZelman

solomonzelman · Answer

I posed the rule,  log(D) C = Log (10) C / Log (10) D

solomonzelman · Answer

*posted

solomonzelman · Answer

well, base 10 is just when the base is unspecified anyway

anonymous · Answer

how do you get D though?

anonymous · Answer

@SolomanZelman