What is log_{10}(x)-4log_{10}(y)+7log_{10}(z) ?

The solution to log_{10}(x)-4log_{10}(y)+7log_{10}(z) is log_{10}((xz^7)/(y^4))

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simplify log_{10}(x)-4log_{10}(y)+7log_{10}(z)

simplify

lo g_{10} (x) - 4 lo g_{10} (y) + 7 lo g_{10} (z)

lo g_{10} (\frac{x z ^{7}}{y ^{4}})

Solution steps

lo g_{10} (x) - 4 lo g_{10} (y) + 7 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}) + 7 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}}) + 7 lo g_{10} (z)

Apply log rule:

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

7 lo g_{10} (z) = lo g_{10} (z^{7})

= lo g_{10} (\frac{x}{y ^{4}}) + lo g_{10} (z^{7})

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^{7}) = lo g_{10} (\frac{x}{y ^{4}} z^{7})

= lo g_{10} (\frac{x}{y ^{4}} z^{7})

Multiply fractions:

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

= lo g_{10} (\frac{x z ^{7}}{y ^{4}})

ln (1) - ln (7 e^{- x})

lo g_{5} (\frac{a ^{3}}{b ^{2}})

\frac{1}{2} (lo g_{6} (x) + lo g_{6} (y))

- lo g_{10} (3.3 \cdot 1 0^{- 6})

2 lo g_{a} (3) - 2 lo g_{a} (2)

What is log_{10}(x)-4log_{10}(y)+7log_{10}(z) ?
The solution to log_{10}(x)-4log_{10}(y)+7log_{10}(z) is log_{10}((xz^7)/(y^4))