## 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

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