What is log_{10}(y/(x^4z^5)) ?

The solution to log_{10}(y/(x^4z^5)) is log_{10}(y)-4log_{10}(x)-5log_{10}(z)

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simplify log_{10}(y/(x^4z^5))

simplify

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

lo g_{10} (y) - 4 lo g_{10} (x) - 5 lo g_{10} (z)

Solution steps

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

Apply log rule:

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

lo g_{10} (\frac{y}{x ^{4} z ^{5}}) = lo g_{10} (y) - lo g_{10} (x^{4} z^{5})

= lo g_{10} (y) - lo g_{10} (x^{4} z^{5})

Simplify

lo g_{10} (x^{4} z^{5}) : 4 lo g_{10} (x) + 5 lo g_{10} (z)

= lo g_{10} (y) - (4 lo g_{10} (x) + 5 lo g_{10} (z))

Apply the distributive law:

- (a + b) = - a - b

- (4 lo g_{10} (x) + 5 lo g_{10} (z)) = - 4 lo g_{10} (x) - 5 lo g_{10} (z)

= lo g_{10} (y) - 4 lo g_{10} (x) - 5 lo g_{10} (z)

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What is log_{10}(y/(x^4z^5)) ?
The solution to log_{10}(y/(x^4z^5)) is log_{10}(y)-4log_{10}(x)-5log_{10}(z)