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 10: Logarithms - Exercise 10.2

Chapter 10 Logarithms
Exercise 10.2 | Q 1.6

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

Simplify : log (a)³÷ log a

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

Write the logarithmic equation for:

V = `(1)/("D"l) sqrt("T"/(pi"r")`

Express the following as a single logarithm:

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

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 log₁₀25 = x and log₁₀27 = y; evaluate without using logarithmic tables, in terms of x and y: log₁₀5

If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: log18

If log 8 = 0.90, find the value of each of the following: log4