What is 5log_{10}(x)+3log_{10}(y)-6log_{10}(z) ?

The solution to 5log_{10}(x)+3log_{10}(y)-6log_{10}(z) is log_{10}((x^5y^3)/(z^6))

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simplify 5log_{10}(x)+3log_{10}(y)-6log_{10}(z)

simplify

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

lo g_{10} (\frac{x ^{5} y ^{3}}{z ^{6}})

Solution steps

5 lo g_{10} (x) + 3 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} (x) = lo g_{10} (x^{5})

= lo g_{10} (x^{5}) + 3 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} (y) = lo g_{10} (y^{3})

= lo g_{10} (x^{5}) + lo g_{10} (y^{3}) - 6 lo g_{10} (z)

Apply log rule:

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

lo g_{10} (x^{5}) + lo g_{10} (y^{3}) = lo g_{10} (x^{5} y^{3})

= lo g_{10} (x^{5} y^{3}) - 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^{5} y^{3}) - 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^{5} y^{3}) - lo g_{10} (z^{6}) = lo g_{10} (\frac{x ^{5} y ^{3}}{z ^{6}})

= lo g_{10} (\frac{x ^{5} y ^{3}}{z ^{6}})

lo g_{10} (\frac{7}{x})

ln (\frac{e ^{- y} y ^{x}}{x !})

lo g_{c} (m) - lo g_{c} (n) - lo g_{c} (z)

2 ln (x) + ln (\frac{x ^{3}}{y ^{2}}) - 4 ln (x + y)

ln (x^{3} + 8) - ln (x + 2) - 2 ln (x^{2} - 2 x + 4)

What is 5log_{10}(x)+3log_{10}(y)-6log_{10}(z) ?
The solution to 5log_{10}(x)+3log_{10}(y)-6log_{10}(z) is log_{10}((x^5y^3)/(z^6))