Simplifying Logarithmic Expressions Questions 3

In this page Simplifying Logarithmic Expressions questions 3 we are going to see solution of third question.

Question 3

Simplify (1/3) log ₃ 27 - log ₃ 81 - 2 log ₃ √3

Solution:

Basic idea : Here totally we have three terms of same bases. Fist let us combine the second third term. For that let us take negative from second and third term.Then we have to bring 2 as power for √3 and (1/3) as power for 27. Then we can simplify using logarithmic formulas.

=  ⅓ log ₃ 27 - log ₃ 81 - 2 log ₃ √3

= log ₃ (27)^ ⅓ - [log ₃ 81 + log ₃ √3²]

= log ₃ (3³)^ - [log ₃ 81 + log ₃ 3]

= log ₃ 3 - [ log ₃ (81 x 3) ]

= log ₃ 3 - log ₃ 243

= log ₃ (3/243)

= log ₃ (1/81)

= log ₃ (1/3⁴)

= log ₃ (3⁻⁴)

= -4 log ₃ 3

= -4 (1)

= -4

Try these problems also

 Question 1Simplify log ₃ 15 - log ₃ 5 + 2 log ₃ 5 Solution Question 2Simplify 2 + 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 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 Quote on Mathematics

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