Question 172949
The rule you need to apply in each case is {{{log(b,(y))=x}}} if and only if {{{b^x=y}}}.


I'll show you the first one:


{{{log(3,(81))=x}}} if and only if {{{3^x=81}}}.  So what does x have to be so that {{{3^x=81}}}?  Since {{{3*3*3*3=3^4=81}}}, {{{x=4}}}.


Work the rest of them the same way.  Note that {{{ln(x)=log(e,(x))}}} ({{{e}}} is the base of the natural logarithms) and {{{log(x)}}} (no base specified) is the same as {{{log(10,(x))}}}


You might also want to make use of the rule {{{log(b,(x^n))=n*log(b,(x))}}} and remember that {{{x^1=x}}} for all real {{{x}}}.