Question 219277
{{{8^(3x-1) = 64^(x+7)}}} Start with the given equation.



{{{8^(3x-1) = (8^2)^(x+7)}}} Rewrite 64 as {{{8^2}}}



{{{8^(3x-1) = 8^(2(x+7))}}} Multiply the exponents.



{{{3x-1=2(x+7)}}} Since the bases are equal, the exponents are equal.



{{{3x-1=2x+14}}} Distribute.



{{{3x=2x+14+1}}} Add {{{1}}} to both sides.



{{{3x-2x=14+1}}} Subtract {{{2x}}} from both sides.



{{{x=14+1}}} Combine like terms on the left side.



{{{x=15}}} Combine like terms on the right side.



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Answer:


So the solution is {{{x=15}}}