Question 78062
a logarithm is essentially an exponent...the base, raised to the power of the logarithm, equals the argument


you can find the log of any argument in any base by dividing the log (common or natural) of the argument by the log of the base...sometimes using natural logs (ln) helps avoid confusion


in your case:  {{{((ln(24))/(ln(2)))-((ln(3))/(ln(2)))=(ln(x))/(ln(5))}}}...using rules for logarithms gives...{{{((ln(24/3))/(ln(2)))*(ln(5))=ln(x)}}}


24/3=8 and since 2^3=8 the first fraction equals 3 giving...3ln(5)=ln(x)...which means 5^3=x...so x=125