Question 735095
{{{10^log(2, (x))=3}}}
One possible solution:
Find the base 10 log of each side:
{{{log((10^log(2, (x))))=log((3))}}}
Now we can use a property of logarithms, {{{log(a, (p^n)) = n*log(a, (p))}}}, to rewrite the left side:
{{{log(2, (x))*log((10))=log((3))}}}
One of the properties of logarithms you should have learned is:
{{{log(a, (a)) = 1}}}
So log(10) = 1:
{{{log(2, (x))=log((3))}}}
Now we rewrite the equation in exponential form. In general {{{log(a, (p)) = n}}} is equivalent to {{{p = a^n}}}. Using this pattern on our equation we get:
{{{x=2^log((3))}}}<br>
If you want/need a decimal approximation for this answer then just enter the expression on the right side into your calculator.