Question 819231
Rewrite it in exponential form:
{{{3 = x^4}}}
4th root of each side:
{{{0+- root(4, 3) = x}}}
(Note: The zero is there <i>only</i> because algebra.com will not let me use the "plus or minus" sign without a number in front. You should not use the zero.)<br>
Check. This is not optional. Use the original equation to check:
{{{log(x, (3)) = 4}}}
Checking {{{x = root(4, 3)}}}:
{{{log(root(4, 3), (3)) = 4}}}
The base is positive but not 1. So it is valid. The argument is positive so it is valid, too. So this solution checks out.
Checking {{{x = -root(4, 3)}}}:
{{{log(-root(4, 3), (3)) = 4}}}
The base is negative. This is an invalid base. So we reject this "solution".<br>
The only solution to your equation is: {{{x = root(4, 3)}}}. (If you need this in the form of a decimal approximation, use {{{3^0.25}}} in your calculator.)