Express the Following as a Single Logarithm: 1 2 Log 25 − 2 Log 3 + Log 36 - Mathematics

Express the following as a single logarithm:

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

Sum

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

= `(1)/(2)"log"5^2 - 2"log"3 + "log"(2^2 xx 3^2)`

= `(1)/(2) xx 2"log"5 - 2"log"3 + "log"2^2 + "log3^2`
= log5 + 2log2
= log5 + log2²
= log5 + log4
= log(5 x 4)
= log20.

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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 5.08

Prove that : If a log b + b log a - 1 = 0, then b^a. a^b = 10

If log (a + 1) = log (4a - 3) - log 3; find a.

Simplify : log (a)³ - log a

Express the following in terms of log 2 and log 3: `"log" root(3)(144)`

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

Express the following as a single logarithm:

`2"log" (16)/(25) - 3 "log" (8)/(5) + "log" 90`

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If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: log540

If x² + y² = 6xy, prove that `"log"((x - y)/2) = (1)/(2)` (log x + log y)