Simplify : Log (A)3 ÷ Log a - Mathematics

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

Given 2 log₁₀ x + 1 = log₁₀ 250, find :
(i) x
(ii) log₁₀ 2x

If log₁₀ a = b, find 10^{3b - 2} in terms of a.

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

Express the following as a single logarithm:

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

Express the following as a single logarithm:

`(1)/(2)"log"25 - 2"log"3 + "log"36`

Express the following as a single logarithm:

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

Simplify the following:

`3"log" (32)/(27) + 5 "log"(125)/(24) - 3"log" (625)/(243) + "log" (2)/(75)`

Simplify the following:

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

If log x = p + q and log y = p - q, find the value of log `(10x)/y^2` in terms of p and q.

If 2 log x + 1 = 40, find: x