Given that log￬10 2 ≈ 0.3010 and log￬10 3 ≈ 0.4771, find each log...

Question

Given that log￬10 2 ≈ 0.3010 and log￬10 3 ≈ 0.4771, find each logarithm without using a calculator. log￬10 6

Accepted Answer

Evaluate the following logarithm by using the approximations, log base eight of three is about 0.5 to 83. And log base eight of 10 is about 1. where we have log base eight of 30. Now to solve this, we will make use of the product property of logarithms which tells us if we have log base A of X multiplied by Y. This can be rewritten as log base A of X plus log base A of Y. Now we notice we have log base 30. We can rewrite our live based state of 30 as a product log base eight of 10 multiplied by three. Now we can apply our products property. You will get log base eight of 10 plus log base eight of three. Now, we know log phase eight of 10, approximates to 1.1073 and log by eight of three approximates to 0.5283. Add those two numbers together. We should get 1.63 which we notice corresponds with answer B OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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Given that log￬10 2 ≈ 0.3010 and log￬10 3 ≈ 0.4771, find each logarithm without using a calculator. log￬10 6