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 7: Logarithms - Exercise 10.2

Chapter 7 Logarithms
Exercise 10.2 | Q 31.1

If log₁₀ 8 = 0.90; find the value of : log 0.125

If log₁₀ 8 = 0.90; find the value of : log√32

Given: log₃ m = x and log₃n = y.

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

Given: log₃ m = x and log₃ n = y.
If 2 log₃ A = 5x - 3y; find A in terms of m and n.

Express the following in terms of log 2 and log 3: `"log"(26)/(51) - "log"(91)/(119)`

Write the logarithmic equation for:

E = `(1)/(2)"m v"^2`

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

If log 27 = 1.431, find the value of the following: log300