What is log_{10}(x)-5log_{10}(y)+6log_{10}(z) ?

The solution to log_{10}(x)-5log_{10}(y)+6log_{10}(z) is log_{10}((xz^6)/(y^5))

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simplify log_{10}(x)-5log_{10}(y)+6log_{10}(z)

simplify

lo g_{10} (x) - 5 lo g_{10} (y) + 6 lo g_{10} (z)

lo g_{10} (\frac{x z ^{6}}{y ^{5}})

Solution steps

lo g_{10} (x) - 5 lo g_{10} (y) + 6 lo g_{10} (z)

Apply log rule:

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

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

= lo g_{10} (x) - lo g_{10} (y^{5}) + 6 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^{5}) = lo g_{10} (\frac{x}{y ^{5}})

= lo g_{10} (\frac{x}{y ^{5}}) + 6 lo g_{10} (z)

Apply log rule:

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

6 lo g_{10} (z) = lo g_{10} (z^{6})

= lo g_{10} (\frac{x}{y ^{5}}) + lo g_{10} (z^{6})

Apply log rule:

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

lo g_{10} (\frac{x}{y ^{5}}) + lo g_{10} (z^{6}) = lo g_{10} (\frac{x}{y ^{5}} z^{6})

= lo g_{10} (\frac{x}{y ^{5}} z^{6})

Multiply fractions:

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

= lo g_{10} (\frac{x z ^{6}}{y ^{5}})

\frac{1}{4} lo g_{b} (x) + 2 lo g_{b} (y) - 3 lo g_{b} (x)

ln (8 x + 4) - 2 ln (2)

lo g_{9} (10) - lo g_{9} (\frac{1}{2}) - lo g_{9} (4)

8.96 \cdot ln (\frac{87}{d - 78})

lo g_{4} (\frac{g}{64})

What is log_{10}(x)-5log_{10}(y)+6log_{10}(z) ?
The solution to log_{10}(x)-5log_{10}(y)+6log_{10}(z) is log_{10}((xz^6)/(y^5))