Simplify: Log A2 + Log A-1

Simplify: log a² + log a^-1

योग

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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अध्याय 7: Logarithms - Exercise 10.2

अध्याय 7 Logarithms
Exercise 10.2 | Q 31.1

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

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

Prove that : (log a)² - (log b)² = log `(( a )/( b ))` . Log (ab)

Express the following in terms of log 2 and log 3: `"log"root(5)(216)`

Write the logarithmic equation for:

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

Express the following as a single logarithm:

`3"log"(5)/(8) + 2"log"(8)/(15) - (1)/(2)"log"(25)/(81) + 3`

Simplify the following:

`2"log" 7 + 3 "log" 5 - "log"(49)/(8)`

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

If x² + y² = 7xy, prove that `"log"((x - y)/3) = (1)/(2)` (log x + log y)

Simplify: log b ÷ log b²