Express the Following in Terms of Log 5 And/Or Log 2: Log125

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

Sum

log125
= log 5³
= 3 log 5.

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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 2.3

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

Given: log₃ m = x and log₃n = y.

Write down `3^(1 - 2y + 3x)` in terms of m and n.

Simplify : log (a)³ - log a

Express the following in terms of log 5 and/or log 2: log160

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

Express the following as a single logarithm:

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

Simplify the following:

`2 "log" 5 +"log" 8 - (1)/(2) "log" 4`

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 x² + y² = 6xy, prove that `"log"((x - y)/2) = (1)/(2)` (log x + log y)

Find the value of:

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