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Popular >

simplify log_{1/3}(sqrt(3))

Solution

simplify

lo g_{\frac{1}{3}} (3)

Solution

- \frac{1}{2}

+1

Solution steps

lo g_{\frac{1}{3}} (3)

Apply log rule:

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

lo g_{\frac{1}{3}} (3) = - lo g_{3} (3)

= - lo g_{3} (3)

Apply radical rule:

a = a^{\frac{1}{2}}

3 = 3^{\frac{1}{2}}

= - lo g_{3} (3^{\frac{1}{2}})

Apply log rule:

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

lo g_{3} (3^{\frac{1}{2}}) = \frac{1}{2}

= - \frac{1}{2}

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Frequently Asked Questions (FAQ)

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