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Popular >

simplify log_{x}(1/32)

Solution

simplify

lo g_{x} (\frac{1}{32})

Solution

- 5 lo g_{x} (2)

Solution steps

lo g_{x} (\frac{1}{32})

\frac{1}{32} = 3 2^{- 1}

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

Apply log rule:

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

lo g_{x} (3 2^{- 1}) = - 1 \cdot lo g_{x} (32)

= - 1 \cdot lo g_{x} (32)

Apply rule:

1 \cdot a = a

= - lo g_{x} (32)

Factor the number:

32 = 2^{5}

= - lo g_{x} (2^{5})

Apply log rule:

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

- lo g_{x} (2^{5}) = - 5 lo g_{x} (2)

= - 5 lo g_{x} (2)

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Frequently Asked Questions (FAQ)

What is log_{x}(1/32) ?
The solution to log_{x}(1/32) is -5log_{x}(2)