Express the Following in Terms of Log 2 and Log 3: Log128

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

Sum

log12⁸
=log (3 x 2²)⁸
= 8log (3 x 2²)
= 8[log 3 + log2²]
= 8[log 3 + 2log 2].

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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 1.6

If log (a + 1) = log (4a - 3) - log 3; find a.

Express the following in terms of log 5 and/or log 2: log125

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

Simplify the following:

`12"log" (3)/(2) + 7 "log" (125)/(27) - 5 "log" (25)/(36) - 7 "log" 25 + "log" (16)/(3)`

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: log 2.25

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 log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: log540

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

Simplify: log a² + log a^-1

Find the value of:

`("log"sqrt(8))/(8)`