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Popular >

simplify log_{10}(4)(1/64)

Solution

simplify

lo g_{10} (4) (\frac{1}{64})

Solution

\frac{1}{32} lo g_{10} (2)

+1

Decimal Notation

0.00940 \dots

Solution steps

lo g_{10} (4) (\frac{1}{64})

Apply rule:

(a) = a

(\frac{1}{64}) = \frac{1}{64}

= lo g_{10} (4) \frac{1}{64}

Factor the number:

4 = 2^{2}

= lo g_{10} (2^{2}) \frac{1}{64}

Apply log rule:

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

lo g_{10} (2^{2}) = 2 lo g_{10} (2)

= 2 lo g_{10} (2) \frac{1}{64}

2 lo g_{10} (2) \frac{1}{64} = \frac{1}{32} lo g_{10} (2)

= \frac{1}{32} lo g_{10} (2)

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Frequently Asked Questions (FAQ)

What is log_{10}(4)(1/64) ?
The solution to log_{10}(4)(1/64) is 1/32 log_{10}(2)