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 10: Logarithms - Exercise 10.2

Chapter 10 Logarithms
Exercise 10.2 | Q 5.03

If log₅ x = y, find 5^{2y+ 3} in terms of x.

If 2 log y - log x - 3 = 0, express x in terms of y.

Express the following in terms of log 2 and log 3: log 216

Express the following in terms of log 5 and/or log 2: log500

Express the following in terms of log 2 and log 3: `"log" root(3)(144)`

Express the following in terms of log 2 and log 3: `"log" root(4)(648)`

Express the following as a single logarithm:

`2"log"(15)/(18) - "log"(25)/(162) + "log"(4)/(9)`

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: log 12

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: `"log"2(1)/(4)`

If x² + y² = 7xy, prove that `"log"((x - y)/3) = (1)/(2)` (log x + log y)