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 √30

Accepted Answer

Evaluate the following logarithm by using the approximation log base eight of is about 1.1073. Have you noticed we have log base eight at the square root of a. Now to solve this, we can rewrite our luck. We have a log base eight of the square of or sure can rewrite our square root a log of base eight of 80 race to the one half power that because we have a log with something raised to a power, we can move our power in front of our log, which is one of our log properties. We can change this then to one half log base eight of 80. Now, we need to make use of our approximation log base state of 10. Let's split up our 80. Actually, we have one half log base eight and we can change our to be eight multiplied by 10. Now, we do have another log property that tells us if we have a log of a multiplied by B inside the parentheses. That is the same as saying log of A plus log of B. So we can change our lives here to be one half multiplied by log base eight of eight plus log base eight of it. Now, we have log base eight of eight since our base and our number are the same, this log evaluates to one. So you have one half multiplied by one plus log by say 10. From here, we can plug in our approximation 1.1073. We then give one half multiplied by 2.1073. Finally multiply or one half gives us 1. are answered and corresponds to answer A 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 √30

Key Concepts

Properties of Logarithms

Change of Base Formula

Square Roots and Exponents

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