Given the exponential equation 3^x=243, what is the logarithmic form of the equation in base 10?

Question

anonymous · Answer

@phi

phi · Answer

take the log (base 10) of both sides

anonymous · Answer

How do I go about doing that?

phi · Answer

$$ \log(3^x)=\log(243) $$

anonymous · Answer

I'm sorry-  I know that's pretty basic stuff, But its been over a month and I forgot most of it.

anonymous · Answer

Is adding the log before the parentheses all you have to do to take the log base 10 of both sides?

phi · Answer

"take the logarithm of x"  means write log(x)
in place of x.

once we have done that, we might want to simplify.  For example, we could use this rule:
$$ \log(a^b) = b \log(a) $$

anonymous · Answer

ok- that would give us
$$xlog(3)=\log(243)$$

anonymous · Answer

right?

anonymous · Answer

@phi

phi · Answer

yes.  and depending on the answer choices, you might want to write it as
$$ x = \frac{\log(243)}{\log(3)} $$

phi · Answer

but they may want the form you wrote down.

anonymous · Answer

That's exactly how it's written, except they included the subscript of 10.  Thank you for the help!