What is simplify-1/3 log_{10}(8) ?

The solution to simplify-1/3 log_{10}(8) is -log_{10}(2)

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simplify-1/3 log_{10}(8)

simplify

- \frac{1}{3} lo g_{10} (8)

- lo g_{10} (2)

Decimal Notation

- 0.30102 \dots

Solution steps

- \frac{1}{3} lo g_{10} (8)

Factor the number:

8 = 2^{3}

= - \frac{1}{3} lo g_{10} (2^{3})

Apply log rule:

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

lo g_{10} (2^{3}) = 3 lo g_{10} (2)

= - \frac{1}{3} \cdot 3 lo g_{10} (2)

- \frac{1}{3} \cdot 3 lo g_{10} (2) = - lo g_{10} (2)

= - lo g_{10} (2)

\frac{x ^{2} - 9}{x ^{2} + x - 20} \cdot \frac{x ^{2} - 8 x + 16}{3 x + 9}

- 15 \div 5

\frac{x + 3}{4} \cdot \frac{3 ( x - 6 )}{3 ( x + 3 )}

(z - i) (z + i)

\frac{\frac{15 a ^{3}}{45 a ^{5}}}{\frac{5 a ^{7}}{9 a ^{4}}}

What is simplify-1/3 log_{10}(8) ?
The solution to simplify-1/3 log_{10}(8) is -log_{10}(2)