Simplify: Log B ÷ Log B2

Simplify: log b ÷ log b²

Sum

log b ÷ log b²
= log b ÷ 2log b
= `("log" "b")/(2"log" "b")`

= `(1)/(2)`.

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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 31.2

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

If log 27 = 1.431, find the value of : log 300

If log₅ x = y, find 5^{2y+ 3} in terms of x.

Write the logarithmic equation for:

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

Express the following as a single logarithm:

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

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 2 log y - log x - 3 = 0, express x in terms of y.

Find the value of:

`("log"sqrt(27) + "log"8 + "log"sqrt(1000))/("log"120)`