Question 202471
# 1


{{{x=log(5,(1))}}} Start with the given equation.



{{{x=log(5,(5^0))}}} Rewrite {{{1}}} as {{{5^0}}}



Note: {{{x^0=1}}} for all any x where {{{x<>0}}}



{{{x=0*log(5,(5))}}} Pull down the exponent using the identity  {{{log(b,(x^y))=y*log(b,(x))}}}



{{{x=0}}} Multiply



So the solution is {{{x=0}}}




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# 2



{{{x=log(e,(sqrt(e)))}}} Start with the given equation.



{{{x=log(e,(e^(1/2)))}}} Convert to exponential notation.



{{{x=(1/2)log(e,(e))}}} Pull down the exponent using the identity  {{{log(b,(x^y))=y*log(b,(x))}}}



{{{x=(1/2)(1)}}} Evaluate the log base "e" of "e" to get 1



{{{x=1/2}}} Multiply



So the solution is {{{x=1/2}}}