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

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

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expand log_{10}((6/5)^6)

expand

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

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

Decimal Notation

0.47508 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

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

lo g_{6} (14) - \frac{1}{2} lo g_{6} (49) + lo g_{6} (18)

ln (\frac{4}{5 x ^{5} y})

lo g_{5} (x) + \frac{1}{3} lo g_{5} (y) - 4 lo g_{5} (z)

lo g_{10} (3 y (5 y + 8))

lo g_{10} (\frac{x}{y ^{6}})

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