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Answer on Algebra Question 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
Expert's answer
By definition of logarithm, the base of logarithm is a positive real number not equal to 1. The equality logx81=-4 is equivalent to 81=x(-4), that is 1/x4=81, or x4=1/81, x4-1/81=0. Seek a positive x, factor the left-hand side (x2-1/9)(x2+1/9)=0,
(x-1/3)(x+1/3)(x2+1/9)=0, x>0. The answer is x=1/3. 

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