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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

lo g_{10} (y^{4}) = 4 lo g_{10} (y)

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

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

Apply the distributive law:

- (a + b) = - a - b

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

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

\frac{1}{4} lo g_{10} (33) + \frac{1}{4} lo g_{10} (44)

lo g_{b} (8 k)

lo g_{10} (1000 x)

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

\frac{1}{3} [5 ln (x + 6) - ln (x) - ln (x^{2} - 25)]

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