Question 23360
Do you know about logarithms?  That is the best way!  Take the ln of both sides:

{{{2.3^x = 48}}}
{{{ln(2.3^x) = ln(48)}}}


Use the property of logarithms that says  {{{log M^N = N log M }}}
{{{ln(2.3^x) = ln(48)}}}
{{{x* ln(2.3) = ln(48)}}}


Now divide both sides of the equation by ln(2.3):

{{{x* ln(2.3) = ln(48)}}}
{{{(x* ln(2.3))/(ln2.3) = ln(48)/(ln2.3)}}}


With a calculator, this is 

x= 4.647807191 (approximately) which rounds off to 4.65.


If you would like to check this (and I would before I embarrass myself to the world by posting another wrong answer!!), you can use a calculator to calculate {{{2.3^(4.6478)}}}.  Using the calculator value of x, it comes out to 48, so it checks!!


R^2 at SCC