Simplify: Log A2 + Log A-1 - Mathematics

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

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b': log 2.25

If log₅ x = y, find 5^{2y+ 3} in terms of x.

Simplify : log (a)³ - log a

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

Write the logarithmic equation for:

n = `sqrt(("M"."g")/("m".l)`

Express the following as a single logarithm:

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

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

If 2 log x + 1 = 40, find: log 5x

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

If log 4 = 0.6020, find the value of each of the following: log8