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Popular >

simplify log_{1/3}(16)

Solution

simplify

lo g_{\frac{1}{3}} (16)

Solution

- 4 lo g_{3} (2)

+1

Decimal Notation

- 2.52371 \dots

Solution steps

lo g_{\frac{1}{3}} (16)

Apply log rule:

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

lo g_{\frac{1}{3}} (16) = - lo g_{3} (16)

= - lo g_{3} (16)

Factor the number:

16 = 2^{4}

= - lo g_{3} (2^{4})

Apply log rule:

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

lo g_{3} (2^{4}) = 4 lo g_{3} (2)

= - 4 lo g_{3} (2)

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Frequently Asked Questions (FAQ)

What is log_{1/3}(16) ?
The solution to log_{1/3}(16) is -4log_{3}(2)