What is (3log_{10}(x)+2log_{10}(y))-6log_{10}(z) ?

The solution to (3log_{10}(x)+2log_{10}(y))-6log_{10}(z) is log_{10}((x^3y^2)/(z^6))

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simplify (3log_{10}(x)+2log_{10}(y))-6log_{10}(z)

simplify

(3 lo g_{10} (x) + 2 lo g_{10} (y)) - 6 lo g_{10} (z)

lo g_{10} (\frac{x ^{3} y ^{2}}{z ^{6}})

Solution steps

(3 lo g_{10} (x) + 2 lo g_{10} (y)) - 6 lo g_{10} (z)

Apply log rule:

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

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

= (lo g_{10} (x^{3}) + 2 lo g_{10} (y)) - 6 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^{3}) + lo g_{10} (y^{2})) - 6 lo g_{10} (z)

Apply log rule:

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

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

= lo g_{10} (x^{3} y^{2}) - 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} (x^{3} y^{2}) - lo g_{10} (z^{6})

Apply log rule:

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

lo g_{10} (x^{3} y^{2}) - lo g_{10} (z^{6}) = lo g_{10} (\frac{x ^{3} y ^{2}}{z ^{6}})

= lo g_{10} (\frac{x ^{3} y ^{2}}{z ^{6}})

2 ln (x + 13) - ln (x + 7)

ln (\frac{0.0205}{0.02})

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

ln (\frac{3}{x})

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

What is (3log_{10}(x)+2log_{10}(y))-6log_{10}(z) ?
The solution to (3log_{10}(x)+2log_{10}(y))-6log_{10}(z) is log_{10}((x^3y^2)/(z^6))