Simplify: Log A2 + Log A-1

Simplify: log a² + log a^-1

Sum

log a² + log a^-1
= 2log a + (-1) log a
= 2log a - log a
= log a (2 - 1)
= log a.

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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 31.1

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

Prove that:

log₁₀ 125 = 3(1 - log₁₀2).

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

Write the logarithmic equation for:

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

Express the following as a single logarithm:
log 18 + log 25 - log 30

Express the following as a single logarithm:

`2 "log" 3 - (1)/(2) "log" 16 + "log" 12`

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: log 75

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

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

If log 4 = 0.6020, find the value of each of the following: log2.5