Use the change-of-base theorem to find an approximation to four d...

Question

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. See Example 8. log_8 0.59

Accepted Answer

Hello, everyone. We are asked to evaluate the following expression and approximate the answer to three significant figures using the change of base theorem. The expression we are given is log base 12 of 77/100. Our answer choices are a negative 0.105 B negative 9.51 C 2.75 D negative 2.75. First recall that the change of base theorem states that if we have a logarithm base A of B, we can take the log of both B and A. As long as we use a different base, meaning we could say it's the log base C of B. And then we have to divide that by the log base C of A. So in our example, we have log base 12 of hundreds. So A is gonna be our 12 B is seven is 70.77. The base I'm gonna use when I do the change of base theorem is gonna be E I do this because then I can take the natural log of 0.77 and divide that by the natural log of 12, I will be using a calculator here to do this division. As I know I'm gonna have a decimal answer. And when I put this in the calculator, I get negative 0. 8091. We do not need all those digits. We only need three significant figures and that will get us to the five in our answer. So after approximating, we end up with negative 0.105 as our answer and that matches answer choice a have a nice day.

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Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. See Example 8. log_8 0.59

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