Simplifying Logarithmic Expressions Questions 6

In this page simplifying logarithmic expressions questions 6 we are going to see solution of sixth question.

Question 6

Simplify ½ log 36 - ⅓ log ₅ 8 + 3 log 2

Solution:

Basic idea : Here totally we have three terms but we have same bases only for two terms .First let us combine them using logarithmic formulas. Then we have to write 3 as power of 2 after that we can combine them. Let us see those steps in the following steps.

= ½ log ₅ 36 - ⅓ log ₅ 8 + 3 log ₈ 2

= log ₅ (36)^½ - log ₅ (8)^⅓ + 3 log ₈ 2

= log ₅ (6²)^½ - log ₅ (2³)^⅓ + 3 log ₈ 2

= log ₅ 6 - log ₅ 2 + 3 log ₈ 2

= log ₅ (6/2) + 3 log ₈ 2

= log ₅ 3 + log ₈ 2³

= log ₅ 3 + log ₈ 8

= log ₅ 3 + 1

= log ₅ 3 + log ₅ 5

= log ₅ (3 x 5)

= log ₅ 15

 Question 1Simplify log ₃ 15 - log ₃ 5 + 2 log ₃ 5 Solution Question 2Simplify 2 + 2 log₂ 5 - 3 log₂ 3 Solution Question 3Simplify 2 log₂ 5 - 3 log₂ 3 Solution Question 4Simplify ½ log ₉ 36+2 log ₉4-3log ₉ 4 Solution Question 5Simplify log ₅ 8 + log ₅ (1/1000) Solution Question 7Simplify 3 + 5 log ₃ 5 Solution Question 8Simplify log ₃ (65/21) + log ₃ (21/13) Solution Question 9Simplify log ₅ 5+log ₅ 20-log ₅24+log ₅ 25 - 3 Solution Question 10Simplify 2 log ₄2+3 log ₂ 5 - log ₂ 15 + log ₂ 7 Solution Quote on Mathematics

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