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

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

If x = (100)^a , y = (10000)^b and z = (10)^c , find log`(10sqrty)/( x^2z^3)` in terms of a, b and c.

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

Express the following in terms of log 2 and log 3: log 216

Express the following as a single logarithm:
log 18 + log 25 - log 30

Express the following as a single logarithm:

`2"log"(9)/(5) - 3"log"(3)/(5) + "log"(16)/(20)`

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 720

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 x = A + B and log y = A-B, express the value of `"log" x^2/(10y)` in terms of A and B.

Simplify: log a² + log a^-1