What is 4log_{10}(xy)-3log_{10}(yz) ?

The solution to 4log_{10}(xy)-3log_{10}(yz) is log_{10}((x^4y)/(z^3))

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simplify 4log_{10}(xy)-3log_{10}(yz)

simplify

4 lo g_{10} (x y) - 3 lo g_{10} (yz)

lo g_{10} (\frac{x ^{4} y}{z ^{3}})

Solution steps

4 lo g_{10} (x y) - 3 lo g_{10} (yz)

Apply log rule:

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

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

= lo g_{10} ((x y)^{4}) - 3 lo g_{10} (yz)

Apply log rule:

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

3 lo g_{10} (yz) = lo g_{10} ((yz)^{3})

= lo g_{10} ((x y)^{4}) - lo g_{10} ((yz)^{3})

Apply log rule:

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

lo g_{10} ((x y)^{4}) - lo g_{10} ((yz)^{3}) = lo g_{10} (\frac{( x y ) ^{4}}{( yz ) ^{3}})

= lo g_{10} (\frac{( x y ) ^{4}}{( yz ) ^{3}})

Simplify

\frac{( x y ) ^{4}}{( yz ) ^{3}} : \frac{x ^{4} y}{z ^{3}}

= lo g_{10} (\frac{x ^{4} y}{z ^{3}})

2 ln (x^{3}) - 3 ln (x)

lo g_{10} (\frac{x}{1000000})

lo g_{10} (2 x) - lo g_{10} (8 x^{3})

lo g_{6} (3 x)

lo g_{b} (\frac{2}{3})

What is 4log_{10}(xy)-3log_{10}(yz) ?
The solution to 4log_{10}(xy)-3log_{10}(yz) is log_{10}((x^4y)/(z^3))