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 9/4

Accepted Answer

Evaluate the following logarithm by using the approximations log base state of three is about 0.5283. And log base eight of 10 is about 1.1073. But we have log base eight of 100 divided by nine possible answers being 0.5851 point 1580.579 and 1.6356. Now, we can take our log base eight of 100 divided by nine and rewrite it. We can rewrite it using the quotient property of logarithms which tells us if we have log base A of X divided by Y. This can be rewritten as log base A of X minus log base A of Y. So we can rewrite our log as live base eight of 100 minus log base eight of nine. Now, we can further simplify our logs by changing our numbers 109. We notice 100 is a perfect square. We can log base eight of 10 square minus log base eight of three square. Now, we can make use of the power property of algorithms which states if we have a log base A of X raced to the R. This is the same thing as saying, R multiplied by log base A of X. This just means we take our exponent and move it in front of our lock. We will then get two base eight of minus two log base eight of three. Now, we can use our approximations log by eight of 10 is 1.1073. So it will say two multiplied by 1. minus two log base eight of three, which is 0.5283. We can we write this further two multiplied by 1.1073 minus 0.5283 and the same parenthesis giving us two multiply them by 0.579, which finally simplifies to 1.158. We don't simplify anymore, which means the answer to our problem is answer B OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Given that log￬10 2 ≈ 0.3010 and log￬10 3 ≈ 0.4771, find each logarithm without using a calculator. log￬10 9/4

Key Concepts

Properties of Logarithms

Change of Base Formula

Logarithmic Values of Powers

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