What is log_{10}((y^6)/z) ?

The solution to log_{10}((y^6)/z) is 6log_{10}(y)-log_{10}(z)

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simplify log_{10}((y^6)/z)

simplify

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

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

Solution steps

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

Apply log rule:

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

lo g_{10} (\frac{y ^{6}}{z}) = lo g_{10} (y^{6}) - lo g_{10} (z)

= lo g_{10} (y^{6}) - lo g_{10} (z)

Simplify

lo g_{10} (y^{6}) : 6 lo g_{10} (y)

= 6 lo g_{10} (y) - lo g_{10} (z)

ln (\frac{2}{5}) - ln (5)

ln (\frac{1}{1 + 4})

- lo g_{10} (5.8 \cdot 1 0^{- 5})

2 lo g_{e} (8) + 9 lo g_{e} (π) - lo g_{e} (5)

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