Q. Which of the following is equivalent to log(m)log9(m) ?Choose 1 answer:(A) log(9)(B) log9(1)(C) log(m)1(D) log(9)1
Recognize logarithm property: Recognize the property of logarithms that can be used to simplify the expression.The expression (log9(m))/(log(m)) can be simplified using the change of base formula for logarithms.The change of base formula states that logb(a)=logc(a)/logc(b), where b and c are bases and a is the argument of the logarithm.
Apply change of base formula: Apply the change of base formula to the given expression.Using the change of base formula, we can rewrite (log9(m))/(log(m)) as:(log9(m))/(log(m))=1/(log(m)/log(9))This is because log9(m) is equivalent to log(m)/log(9) by the change of base formula.
Simplify the expression: Simplify the expression.Simplifying the expression, we get:(log(9)log(m))1=log(m)log(9)This simplifies to:(log(m)log(9))=(log(9)log(m))1
Identify correct answer: Identify the correct answer from the given options.The simplified expression (log(9)log(m))1 matches option (D) log(9)1.