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Popular >

simplify log_{1/2}(9)

Solution

simplify

lo g_{\frac{1}{2}} (9)

Solution

- 2 lo g_{2} (3)

+1

Decimal Notation

- 3.16992 \dots

Solution steps

lo g_{\frac{1}{2}} (9)

Apply log rule:

lo g_{\frac{1}{a}} (x) = - lo g_{a} (x)

lo g_{\frac{1}{2}} (9) = - lo g_{2} (9)

= - lo g_{2} (9)

Factor the number:

9 = 3^{2}

= - lo g_{2} (3^{2})

Apply log rule:

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

lo g_{2} (3^{2}) = 2 lo g_{2} (3)

= - 2 lo g_{2} (3)

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Frequently Asked Questions (FAQ)

What is log_{1/2}(9) ?
The solution to log_{1/2}(9) is -2log_{2}(3)