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_1/2 3

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 1/ of seven. Our answer choices are a 1. B negative 1.40 C 0.712 D negative 0.712. First recall the, the change of base theorem states that if we have a logarithm base A of B, we can change the base by using a third value. So we could do the log base C of B divided by the log base C of A. So for our example, where we have log base 1/4 of seven, I'm gonna pick E as my extra base. That way I can write this as the natural log of seven divided by the natural log of 1/4. I will be using a calculator to find the decimals here. And when I use my calculator and I type the natural log of seven divided by the natural log of 1/4 I get negative 1.403677461, we don't need all of those digits. We only need three significant figures. So we're going to round this to the 100th place which gives us the value negative 1.40. So that is our answer and it is answer choice B 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_1/2 3