What is log_{10}(x)-8log_{10}(y)+9log_{10}(z) ?

The solution to log_{10}(x)-8log_{10}(y)+9log_{10}(z) is log_{10}((xz^9)/(y^8))

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simplify log_{10}(x)-8log_{10}(y)+9log_{10}(z)

simplify

lo g_{10} (x) - 8 lo g_{10} (y) + 9 lo g_{10} (z)

lo g_{10} (\frac{x z ^{9}}{y ^{8}})

Solution steps

lo g_{10} (x) - 8 lo g_{10} (y) + 9 lo g_{10} (z)

Apply log rule:

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

8 lo g_{10} (y) = lo g_{10} (y^{8})

= lo g_{10} (x) - lo g_{10} (y^{8}) + 9 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^{8}) = lo g_{10} (\frac{x}{y ^{8}})

= lo g_{10} (\frac{x}{y ^{8}}) + 9 lo g_{10} (z)

Apply log rule:

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

9 lo g_{10} (z) = lo g_{10} (z^{9})

= lo g_{10} (\frac{x}{y ^{8}}) + lo g_{10} (z^{9})

Apply log rule:

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

lo g_{10} (\frac{x}{y ^{8}}) + lo g_{10} (z^{9}) = lo g_{10} (\frac{x}{y ^{8}} z^{9})

= lo g_{10} (\frac{x}{y ^{8}} z^{9})

Multiply fractions:

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

= lo g_{10} (\frac{x z ^{9}}{y ^{8}})

lo g_{10} (7 a) + lo g_{10} (6 b)

3 (lo g_{7} (x) + 3 lo g_{7} (y) - 4 lo g_{7} (z))

2 ln (x) + 4 ln (y) - 5 ln (z)

lo g_{4} (5 x y)

lo g_{b} (x^{2} y^{3})

What is log_{10}(x)-8log_{10}(y)+9log_{10}(z) ?
The solution to log_{10}(x)-8log_{10}(y)+9log_{10}(z) is log_{10}((xz^9)/(y^8))