What is log_{10}(y/(z^9)) ?

The solution to log_{10}(y/(z^9)) is log_{10}(y)-9log_{10}(z)

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simplify log_{10}(y/(z^9))

simplify

lo g_{10} (\frac{y}{z ^{9}})

lo g_{10} (y) - 9 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{y}{z ^{9}})

Apply log rule:

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

lo g_{10} (\frac{y}{z ^{9}}) = lo g_{10} (y) - lo g_{10} (z^{9})

= lo g_{10} (y) - lo g_{10} (z^{9})

Simplify

lo g_{10} (z^{9}) : 9 lo g_{10} (z)

= lo g_{10} (y) - 9 lo g_{10} (z)

- lo g_{10} (8 \cdot 1 0^{- 8})

lo g_{10} (\frac{1 0 ^{x}}{x ( x ^{2} + 1 ) ( x ^{4} + 2 )})

5 ln (x) + 2 ln (y)

- lo g_{10} (4.2 \times 1 0^{- 3})

- ln (x + 2) + 2 ln (x + 3)

What is log_{10}(y/(z^9)) ?
The solution to log_{10}(y/(z^9)) is log_{10}(y)-9log_{10}(z)