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Popular >

simplify log_{1/3}(0.5)

Solution

simplify

lo g_{\frac{1}{3}} (0.5)

Solution

lo g_{3} (2)

+1

Decimal Notation

0.63092 \dots

Solution steps

lo g_{\frac{1}{3}} (0.5)

Apply log rule:

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

lo g_{\frac{1}{3}} (0.5) = - lo g_{3} (0.5)

= - lo g_{3} (0.5)

0.5 = \frac{5}{10}

= - lo g_{3} (\frac{5}{10})

Cancel the numbers:

\frac{5}{10} = \frac{1}{2}

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

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

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

Apply log rule:

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

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

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

Apply rule:

1 \cdot a = a

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

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

Apply rule

- (- a) = a

= lo g_{3} (2)

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Frequently Asked Questions (FAQ)

What is log_{1/3}(0.5) ?
The solution to log_{1/3}(0.5) is log_{3}(2)