Question 133341
{{{log(3,(3^(m+1)+3^(m+2)))= log(3,(972))}}} Start with the given equation



{{{3^(log(3,(3^(m+1)+3^(m+2))))= 3^(log(3,(972)))}}} Raise both sides as exponents with bases of 3. This will eliminate the logs



{{{3^(m+1)+3^(m+2)= 972}}} Simplify



{{{3^(m)*3^(1)+3^(m)*3^(2)= 972}}} Break up the left side using the identity {{{x^(y+z)=x^y*x^z}}}



{{{3^(m)*3+3^(m)*9= 972}}} Evaluate {{{3^1}}} to get 3. Evaluate {{{3^2}}} to get 9



{{{3*3^(m)(1+3)= 972}}} Factor out the GCF



{{{3*3^(m)(4)= 972}}} Add



{{{3*3^(m)= 243}}} Divide both sides by 4



{{{3^(m)= 81}}} Divide both sides by 3



{{{3^(m)= 3^4}}} Rewrite 81 as {{{3^4}}}



Since the bases are equal, this means that the exponents are equal. So {{{m=4}}}



So our answer is {{{m=4}}}