Question 187010
{{{log(x,(x^2 - x + 4))=2}}} Start with the given equation.



{{{x^2=x^2 - x + 4}}} Rewrite the equation using the property: {{{log(b,(x))=y}}} ====> {{{b^y=x}}}



{{{x^2-x^2 + x = 4}}} Subtract {{{x^2}}} from both sides. Add "x" to both sides.



{{{x = 4}}} Combine like terms.




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Answer:


So the answer is {{{x=4}}}



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# 2



{{{3 + log(3,(243)) = 3x - 4}}} Start with the given equation.



{{{3 + log(3,(3^5)) = 3x - 4}}} Rewrite {{{243}}} as {{{3^5}}}



{{{3 + 5*log(3,(3)) = 3x - 4}}} Rewrite the log using the identity  {{{log(b,(x^y))=y*log(b,(x))}}}



{{{3 + 5(1) = 3x - 4}}} Evaluate the log base 3 of 3 to get 1



{{{3 + 5 = 3x - 4}}} Multiply



{{{8=3x-4}}} Combine like terms on the left side.



{{{8+4=3x}}} Add 4 to both sides.



{{{12=3x}}} Combine like terms.



{{{12/3=x}}} Divide both sides by 3.



{{{4=x}}} Reduce




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Answer:


So the answer is {{{x=4}}}