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 3( log 5 - log 3 ) - ( log 5 - 2 log 6 ) = 2 - log x, find x.

If log (a + b) = log a + log b, find a in terms of b.

If log₁₀ a = b, find 10^{3b - 2} in terms of a.

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

Write the logarithmic equation for:

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

Express the following as a single logarithm:

`"log"(81)/(8) - 2"log"(3)/(5) + 3"log"(2)/(5) + "log"(25)/(9)`

Simplify the following:

`12"log" (3)/(2) + 7 "log" (125)/(27) - 5 "log" (25)/(36) - 7 "log" 25 + "log" (16)/(3)`

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

If log 8 = 0.90, find the value of each of the following: log4

Find the value of:

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