Express the Following as a Single Logarithm: 2 Log 3 − 1 2 Log 16 + Log 12

Express the following as a single logarithm:

`2 "log" 3 - (1)/(2) "log" 16 + "log" 12`

Sum

`2 "log" 3 - (1)/(2) "log" 16 + "log" 12`

= `2 "log" 3 - (1)/(2) "log" 2^4 + "log" (2^2 xx 3)`

= `2 "log" 3 - (1)/(2) xx 4 "log" 2 + "log" 2^2 + "log" 3`

= 2 log 3 - 2 log 2 + 2 log 2 + log 3
= 3 log 3
= log 3³
= log 27.

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Expansion of Expressions with the Help of Laws of Logarithm

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Chapter 7: Logarithms - Exercise 10.2

Chapter 7 Logarithms
Exercise 10.2 | Q 5.03

If log 2 = 0.3010 and log 3 = 0.4771 ; find the value of : log 1.2

Prove that : If a log b + b log a - 1 = 0, then b^a. a^b = 10

Express the following in terms of log 2 and log 3: log 144

Express the following in terms of log 2 and log 3: log12⁸

Express the following in terms of log 5 and/or log 2: log80

Express the following in terms of log 2 and log 3: `"log"(225)/(16) - 2"log"(5)/(9) + "log"(2/3)^5`

Express the following as a single logarithm:

`2"log"(9)/(5) - 3"log"(3)/(5) + "log"(16)/(20)`

If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: log45

If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: `"log" sqrt(72)`

If log 27 = 1.431, find the value of the following: log 9