What is 3log_{10}(x)+2log_{10}(y)-5log_{10}(z) ?

The solution to 3log_{10}(x)+2log_{10}(y)-5log_{10}(z) is log_{10}((x^3y^2)/(z^5))

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simplify 3log_{10}(x)+2log_{10}(y)-5log_{10}(z)

simplify

3 lo g_{10} (x) + 2 lo g_{10} (y) - 5 lo g_{10} (z)

lo g_{10} (\frac{x ^{3} y ^{2}}{z ^{5}})

Solution steps

3 lo g_{10} (x) + 2 lo g_{10} (y) - 5 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) - 5 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}) - 5 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}) - 5 lo g_{10} (z)

Apply log rule:

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

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

= lo g_{10} (x^{3} y^{2}) - lo g_{10} (z^{5})

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^{5}) = lo g_{10} (\frac{x ^{3} y ^{2}}{z ^{5}})

= lo g_{10} (\frac{x ^{3} y ^{2}}{z ^{5}})

2 ln (3) - ln (2)

2 ln (3) - ln (5)

2 lo g_{10} (3 x) - lo g_{10} (7 x)

5 ln (x) + 3 ln (y) - 2 ln (z)

lo g_{10} (\frac{y ^{4}}{x ^{5} z})

What is 3log_{10}(x)+2log_{10}(y)-5log_{10}(z) ?
The solution to 3log_{10}(x)+2log_{10}(y)-5log_{10}(z) is log_{10}((x^3y^2)/(z^5))