Logarithms

We are given the equation . We know that . Now we simplify using the change of base formula: Simplifying this further, we find that: Thus, the correct answer is .

Using the logarithmic property , we can simplify the expression: Simplifying inside the logarithm: Thus, the expression becomes . Therefore, the correct answer is 0.

We are asked to find . First, express 125 as a power of 5: Therefore: Using the logarithmic property : Thus, the correct answer is .

We are given the expression . Using logarithmic properties: Thus, the expression becomes: Multiplying: After simplification, it is evident that the expression evaluates to 0. Hence, the correct answer is 0.