Simplify : Log (A)3 ÷ Log a

Simplify : log (a)³÷ log a

Sum

log (a)³÷ log a
= 3 log a ÷ log a
= `(3 log a)/(log a)`
= 3

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Expansion of Expressions with the Help of Laws of Logarithm

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Chapter 8: Logarithms - Exercise 8 (C) [Page 108]

Chapter 8 Logarithms
Exercise 8 (C) | Q 6.2 | Page 108

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

Given log x = 2m - n , log y = n - 2m and log z = 3m - 2n , find in terms of m and n, the value of log `(x^2y^3 ) /(z^4) `.

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

Express the following in terms of log 2 and log 3: `"log"root(5)(216)`

Express the following as a single logarithm:

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

Express the following as a single logarithm:

`"log"(81)/(8) - 2"log"(3)/(5) + 3"log"(2)/(5) + "log"(25)/(9)`

If log a = p and log b = q, express `"a"^3/"b"^2` in terms of p and q.

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

Find the value of:

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

Find the value of:

`("log"sqrt125 - "log"sqrt(27) - "log"sqrt(8))/("log"6 - "log"5)`