Question 113513
I'm not certain what you mean by "expanded notation" but I suspect that it means "raised to the power of", so, with that in mind, let's proceed...
{{{5^x = 72}}} Take the logarithm of both sides.
{{{Log(5^x) = Log(72)}}} Apply the power rule for logarithms to the left side:{{{Log[b](M^p) = p*Log[b](M)}}}.
{{{x*Log(5) = log((72))}}} Divide both sides by log(5).
{{{x = log((72))/Log(5)}}}
{{{x = 2.657}}}

Check:
{{{5^x = 72}}} Substitute x = 2.657
{{{5^2.657 = 71.995}}}