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Popular >

simplify log_{0.5}(100)

Solution

simplify

lo g_{0.5} (100)

Solution

- 2 - 2 lo g_{2} (5)

+1

Decimal Notation

- 6.64385 \dots

Solution steps

lo g_{0.5} (100)

Factor the number:

100 = 1 0^{2}

= lo g_{0.5} (1 0^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{0.5} (1 0^{2}) = 2 lo g_{0.5} (10)

= 2 lo g_{0.5} (10)

Simplify

lo g_{0.5} (10) : - lo g_{2} (10)

= 2 (- lo g_{2} (10))

Remove parentheses:

(- a) = - a

= - 2 lo g_{2} (10)

lo g_{2} (10) = 1 + lo g_{2} (5)

= - 2 (1 + lo g_{2} (5))

Expand

- 2 (1 + lo g_{2} (5)) : - 2 - 2 lo g_{2} (5)

= - 2 - 2 lo g_{2} (5)

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Frequently Asked Questions (FAQ)

What is log_{0.5}(100) ?
The solution to log_{0.5}(100) is -2-2log_{2}(5)