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Popular >

simplify log_{1/2}(sqrt(8))

Solution

simplify

lo g_{\frac{1}{2}} (8)

Solution

- \frac{3}{2}

+1

Solution steps

lo g_{\frac{1}{2}} (8)

Apply log rule:

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

lo g_{\frac{1}{2}} (8) = - lo g_{2} (8)

= - lo g_{2} (8)

8 = 2^{\frac{3}{2}}

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

Apply log rule:

lo g_{a} (a^{b}) = b

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

= - \frac{3}{2}

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Frequently Asked Questions (FAQ)

What is log_{1/2}(sqrt(8)) ?
The solution to log_{1/2}(sqrt(8)) is -3/2