What is log_{10}((z^2sqrt(y))/(x^2)) ?

The solution to log_{10}((z^2sqrt(y))/(x^2)) is 2log_{10}(z)+log_{10}(sqrt(y))-2log_{10}(x)

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simplify log_{10}((z^2sqrt(y))/(x^2))

simplify

lo g_{10} (\frac{z ^{2} y}{x ^{2}})

2 lo g_{10} (z) + lo g_{10} (y) - 2 lo g_{10} (x)

Solution steps

lo g_{10} (\frac{z ^{2} y}{x ^{2}})

Apply log rule:

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

lo g_{10} (\frac{z ^{2} y}{x ^{2}}) = lo g_{10} (z^{2} y) - lo g_{10} (x^{2})

= lo g_{10} (z^{2} y) - lo g_{10} (x^{2})

lo g_{10} (z^{2} y) = 2 lo g_{10} (z) + lo g_{10} (y)

lo g_{10} (x^{2}) = 2 lo g_{10} (x)

= 2 lo g_{10} (z) + lo g_{10} (y) - 2 lo g_{10} (x)

lo g_{3} (\frac{4 y}{z})

ln (z) - ln (16)

lo g_{7} (8) + lo g_{7} (5)

2 lo g_{10} (x) - 4 lo g_{10} (x + 1) - 3 lo g_{10} (5 x) + \frac{1}{3} lo g_{10} (x - 1)

(2) lo g_{10} (3 x^{2}) - lo g_{10} (2 x^{2} - 1)

What is log_{10}((z^2sqrt(y))/(x^2)) ?
The solution to log_{10}((z^2sqrt(y))/(x^2)) is 2log_{10}(z)+log_{10}(sqrt(y))-2log_{10}(x)