What is log_{10}(x)-4log_{10}(y)+5log_{10}(z) ?

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

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simplify log_{10}(x)-4log_{10}(y)+5log_{10}(z)

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

ln (\frac{r}{6 s})

lo g_{10} (\frac{5 a}{3 b})

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

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

lo g_{10} (\frac{\frac{1}{100} ( x ^{2} + 1 )}{x ^{4} ( x + 1 )})

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