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Popular >

simplify log_{1/3}(sqrt(243))

Solution

simplify

lo g_{\frac{1}{3}} (243)

Solution

- \frac{5}{2}

+1

Decimal Notation

- 2.5

Solution steps

lo g_{\frac{1}{3}} (243)

Apply log rule:

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

lo g_{\frac{1}{3}} (243) = - lo g_{3} (243)

= - lo g_{3} (243)

243 = 3^{\frac{5}{2}}

= - lo g_{3} (3^{\frac{5}{2}})

Apply log rule:

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

lo g_{3} (3^{\frac{5}{2}}) = \frac{5}{2}

= - \frac{5}{2}

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Frequently Asked Questions (FAQ)

What is log_{1/3}(sqrt(243)) ?
The solution to log_{1/3}(sqrt(243)) is -5/2