## simplifying logarithmic expressions questions 10

In this page simplifying logarithmic expressions questions 10 we are going to see solution of tenth question.

Question 10

Simplify 2 log 2 + 3 log ₂ 5 -  log ₂ 15 + log ₂ 7

Solution:

Basic idea : Here totally we have four terms out of these three terms have same bases. First we have to combine them by using logarithmic formulas. Then we have to change base of first term as others.

= 2 log 2 + 3 log ₂ 5 -  log ₂ 15 + log ₂ 7

= log 2² + log ₂ 5³ -  log ₂ 15 + log ₂ 7

= log 4 + log ₂ 125 log ₂ 15 + log ₂ 7

=  1 + log ₂ 125 + log ₂ 7 log ₂ 15

= 1 + log ₂ (125 x 7) log ₂ 15

= log ₂ 2 + log ₂ 875 log ₂ 15

= log ₂ 2 + log ₂ (875/15)

= log ₂ 2 + log ₂ (175/3)

= log ₂ (2 x 175)/3

= log ₂ (2 x 175)/3

= log ₃ (350/3)

Try these questions 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 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 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 simplifying logarithmic expressions questions 10 Question 9Simplify log ₅ 5+log ₅ 20-log ₅24+log ₅ 25 - 3 Solution

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