What is log_{10}((6/11)^5) ?

The solution to log_{10}((6/11)^5) is 5log_{10}(6)-5log_{10}(11)

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simplify log_{10}((6/11)^5)

simplify

lo g_{10} ((\frac{6}{11})^{5})

5 lo g_{10} (6) - 5 lo g_{10} (11)

Solution steps

lo g_{10} ((\frac{6}{11})^{5})

Apply log rule:

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

lo g_{10} ((\frac{6}{11})^{5}) = 5 lo g_{10} (\frac{6}{11})

= 5 lo g_{10} (\frac{6}{11})

Apply log rule:

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

lo g_{10} (\frac{6}{11}) = lo g_{10} (6) - lo g_{10} (11)

= 5 (lo g_{10} (6) - lo g_{10} (11))

Apply the distributive law:

a (b - c) = ab - a c

5 (lo g_{10} (6) - lo g_{10} (11)) = 5 lo g_{10} (6) - 5 lo g_{10} (11)

= 5 lo g_{10} (6) - 5 lo g_{10} (11)

\frac{1}{2} \div \frac{1}{6}

lo g_{2} (2000)

64 - 121 x^{2}

\frac{3 x + 2}{x - 7} - \frac{2 x}{x ^{2} - 5 x - 14}

lo g_{5} (5^{\frac{1}{4}})

What is log_{10}((6/11)^5) ?
The solution to log_{10}((6/11)^5) is 5log_{10}(6)-5log_{10}(11)