Question 388347
{{{4^(k-2)=8^(12-k)}}} Start with the given equation.



{{{(2^2)^(k-2)=8^(12-k)}}} Rewrite 4 as {{{2^2}}}



{{{(2^2)^(k-2)=(2^3)^(12-k)}}} Rewrite 8 as {{{2^3}}}



{{{2^(2(k-2))=2^(3(12-k))}}} Multiply the exponents.



{{{2(k-2)=3(12-k)}}} Since the bases are equal, the exponents are equal.



{{{2k-4=36-3k}}} Distribute.



{{{2k=36-3k+4}}} Add {{{4}}} to both sides.



{{{2k+3k=36+4}}} Add {{{3k}}} to both sides.



{{{5k=36+4}}} Combine like terms on the left side.



{{{5k=40}}} Combine like terms on the right side.



{{{k=(40)/(5)}}} Divide both sides by {{{5}}} to isolate {{{k}}}.



{{{k=8}}} Reduce.



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Answer:


So the solution is {{{k=8}}} 



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