What is log_{10}((sqrt(y)z^4)/x) ?

The solution to log_{10}((sqrt(y)z^4)/x) is log_{10}(sqrt(y))+4log_{10}(z)-log_{10}(x)

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simplify log_{10}((sqrt(y)z^4)/x)

simplify

lo g_{10} (\frac{y z ^{4}}{x})

lo g_{10} (y) + 4 lo g_{10} (z) - lo g_{10} (x)

Solution steps

lo g_{10} (\frac{y z ^{4}}{x})

Apply log rule:

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

lo g_{10} (\frac{y z ^{4}}{x}) = lo g_{10} (y z^{4}) - lo g_{10} (x)

= lo g_{10} (y z^{4}) - lo g_{10} (x)

Simplify

lo g_{10} (y z^{4}) : lo g_{10} (y) + 4 lo g_{10} (z)

= lo g_{10} (y) + 4 lo g_{10} (z) - lo g_{10} (x)

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

lo g_{10} (x^{\frac{3}{5}} y^{4})

lo g_{10} (x^{3} \cdot y^{- 2})

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

What is log_{10}((sqrt(y)z^4)/x) ?
The solution to log_{10}((sqrt(y)z^4)/x) is log_{10}(sqrt(y))+4log_{10}(z)-log_{10}(x)