What is log_{10}(y/(z^5)) ?

The solution to log_{10}(y/(z^5)) is log_{10}(y)-5log_{10}(z)

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simplify log_{10}(y/(z^5))

simplify

lo g_{10} (\frac{y}{z ^{5}})

lo g_{10} (y) - 5 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{y}{z ^{5}})

Apply log rule:

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

lo g_{10} (\frac{y}{z ^{5}}) = lo g_{10} (y) - lo g_{10} (z^{5})

= lo g_{10} (y) - lo g_{10} (z^{5})

Simplify

lo g_{10} (z^{5}) : 5 lo g_{10} (z)

= lo g_{10} (y) - 5 lo g_{10} (z)

lo g_{10} (\frac{4 x}{3})

lo g_{6} (x^{2} - 36) - lo g_{6} (x - 6)

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

ln^{2} (x) - 2 ln (x)

lo g_{3} (\frac{9 b ^{3} y ^{2} - 7}{y ( x + 7 ) ^{2}})

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