Question 116158
#1

{{{log(3,(x))=-2}}} Start with the given equation. 



{{{3^(-2)=x}}} Rewrite the equation using the property: {{{log(b,(x))=y}}} ====> {{{b^y=x}}}



{{{1/3^2=x}}} Rewrite {{{3^(-2)}}} as {{{1/3^2}}}



{{{1/9=x}}} Evaluate {{{3^2}}} to get 9


So our answer is {{{x=1/9}}}


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#2


{{{7^x=8}}} Start with the given equation.



{{{log(10,(7^x))=log(10,(8))}}} Take the log of both sides.




{{{x*log(10,(7))=log(10,(8))}}} Rewrite the left side using the identity  {{{log(b,(x^y))=y*log(b,(x))}}} .




{{{x=log(10,(8))/log(10,(7))}}} Divide both sides by {{{log(10,(7))}}} to isolate x



{{{x=1.06862156132407}}} Now simply use a calculator to evaluate the right side


So our approximate answer is {{{x=1.07}}}