What is 4log_{10}(x)+3log_{10}(y)-2log_{10}(z) ?

The solution to 4log_{10}(x)+3log_{10}(y)-2log_{10}(z) is log_{10}((x^4y^3)/(z^2))

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simplify 4log_{10}(x)+3log_{10}(y)-2log_{10}(z)

simplify

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

lo g_{10} (\frac{x ^{4} y ^{3}}{z ^{2}})

Solution steps

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

Apply log rule:

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

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

= lo g_{10} (x^{4}) + 3 lo g_{10} (y) - 2 lo g_{10} (z)

Apply log rule:

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

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

= lo g_{10} (x^{4}) + lo g_{10} (y^{3}) - 2 lo g_{10} (z)

Apply log rule:

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

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

= lo g_{10} (x^{4} y^{3}) - 2 lo g_{10} (z)

Apply log rule:

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

2 lo g_{10} (z) = lo g_{10} (z^{2})

= lo g_{10} (x^{4} y^{3}) - lo g_{10} (z^{2})

Apply log rule:

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

lo g_{10} (x^{4} y^{3}) - lo g_{10} (z^{2}) = lo g_{10} (\frac{x ^{4} y ^{3}}{z ^{2}})

= lo g_{10} (\frac{x ^{4} y ^{3}}{z ^{2}})

3 ln (\frac{a}{2}) + 2 ln (2 b)

\frac{1}{2} ln (\frac{3}{4})

4 lo g_{2} (x) + lo g_{2} (3) - 2 lo g_{2} (x^{2})

lo g_{3} (x^{5} y^{3})

ln (\frac{134.8}{15})

What is 4log_{10}(x)+3log_{10}(y)-2log_{10}(z) ?
The solution to 4log_{10}(x)+3log_{10}(y)-2log_{10}(z) is log_{10}((x^4y^3)/(z^2))