Evaluate ( log of 9)/( log of 3)

Problem

(log_)(9)/(log_)(3)

Solution

1. Identify the expression as a quotient of logarithms with the same base.

2. Apply the change of base formula in reverse, which states (log_b)(a)/(log_b)(c)=(log_c)(a)

3. Rewrite the expression using this rule:

(log_)(9)/(log_)(3)=(log_3)(9)

4. Evaluate the logarithm by determining the power to which the base 3 must be raised to obtain 9

5. Recognize that 3=9

(log_3)(3)=2

Final Answer

(log_)(9)/(log_)(3)=2

Want more problems? Check here!