# Answer to Question #43114 in Algebra for Alice

Question #43114

What value will make the equation true? Logx 81= -4

A) x= 1/9

B) x= 1/3

C) x=3

D) x=9

A) x= 1/9

B) x= 1/3

C) x=3

D) x=9

Expert's answer

By definition of logarithm, the base of logarithm is a positive real number not equal to 1. The equality log

(x-1/3)(x+1/3)(x

_{x}81=-4 is equivalent to 81=x^{(-4)}, that is 1/x^{4}=81, or x^{4}=1/81, x^{4}-1/81=0. Seek a positive x, factor the left-hand side (x^{2}-1/9)(x^{2}+1/9)=0,(x-1/3)(x+1/3)(x

^{2}+1/9)=0, x>0. The answer is x=1/3. Need a fast expert's response?

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