Solving Logarithmic Equations Using Technology — Quiz
Question 9 • Mathematics III
Which expression can be used to approximate the expression, for all positive numbers A , b , and x , where A is not equal to 1 and b is not equal to 1 ? the log base A of x
Answer
A
the fraction with numerator the log base A of b and denominator the log base x of b
B
the fraction with numerator the log base b of x and denominator the log base b of A
C
the fraction with numerator the log base b of A and denominator the log base b of x
D
the fraction with numerator the log base A of x and denominator the log base b of x
Explanation
By the change-of-base formula, log base A of x equals (log base b of x) divided by (log base b of A). The base b can be any valid logarithm base, so this expression works for positive A, b, and x when A and b are not 1 (with the logarithms defined). Thus, choice A, the fraction with log base b of x in the numerator and log base b of A in the denominator, is correct.
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