What is log_{10}(x)-2log_{10}(y)+5log_{10}(z) ?

The solution to log_{10}(x)-2log_{10}(y)+5log_{10}(z) is log_{10}((xz^5)/(y^2))

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simplify log_{10}(x)-2log_{10}(y)+5log_{10}(z)

simplify

lo g_{10} (x) - 2 lo g_{10} (y) + 5 lo g_{10} (z)

lo g_{10} (\frac{x z ^{5}}{y ^{2}})

Solution steps

lo g_{10} (x) - 2 lo g_{10} (y) + 5 lo g_{10} (z)

Apply log rule:

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

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

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

= lo g_{10} (\frac{x}{y ^{2}}) + 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 ^{2}}) + 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 ^{2}}) + lo g_{10} (z^{5}) = lo g_{10} (\frac{x}{y ^{2}} z^{5})

= lo g_{10} (\frac{x}{y ^{2}} z^{5})

Multiply fractions:

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

= lo g_{10} (\frac{x z ^{5}}{y ^{2}})

lo g_{10} (\frac{2 x + y}{y ^{3}})

lo g_{2} (5) + lo g_{2} (2 x - 3)

lo g_{10} (100 y^{4} \cdot \frac{y + 5}{y - 5})

lo g_{10} (x) + lo g_{10} (5)

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

What is log_{10}(x)-2log_{10}(y)+5log_{10}(z) ?
The solution to log_{10}(x)-2log_{10}(y)+5log_{10}(z) is log_{10}((xz^5)/(y^2))