Question 191772
{{{1000^(8x)=100}}} Start with the given equation.



{{{(10^3)^(8x)=10^2}}} Rewrite 1000 as {{{10^3}}} and 100 as {{{10^2}}}



{{{10^(3(8x))=10^2}}} Multiply the exponents.



{{{10^(24x)=10^2}}} Multiply



{{{24x=2}}} Since the bases are equal, this means that the exponents are equal.



{{{x=(2)/(24)}}} Divide both sides by {{{24}}} to isolate {{{x}}}.



{{{x=1/12}}} Reduce.



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Answer:


So the answer is {{{x=1/12}}} which approximates to {{{x=0.083}}}.