## Simplifying Logarithmic Expressions Questions 4

In this page Simplifying Logarithmic Expressions questions 4 we are going to see solution of first question.

Question 4

Simplify ½ log 36 + 2 log ₉ 4 - 3 log ₉ 4

Solution:

Basic idea : Here totally we have three terms of same bases. So we have to combine them by using logarithmic formulas.Fist we have to write 1/2 as power of 36 and 2 as power of 4. After combining the first two terms we can consider the third. let us see the steps in detail below.

= (½) log ₉ 36 + 2 log ₉ 4 - 3 log ₉ 4

= log ₉ (36)^½ + log ₉ 4² - 3 log ₉ 4

= log ₉ (6²)^½ + log ₉ 16 - 3 log ₉ 4

= log ₉ 6 + log ₉ 16 - 3 log ₉ 4

= log ₉ (6 x 16) log ₉ 4³

= log ₉ (6 x 16) log ₉ 64

= log ₉ [ (6 x 16)/64 ]

= log ₉ [ 6/4 ]

= log ₉ [ 3/2 ]

 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 5Simplify log ₅ 8 + log ₅ (1/1000) Solution Question 6Simplify ½ log ₅ 36 - ⅓ log ₅ 8 + 3 log ₈ 2 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

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