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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

Apply log rule:

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

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

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

6 [ln (z) + ln (z + 7)] - 3 ln (z - 7)

ln (x \frac{y}{2})

9 ln (x) - \frac{1}{2} ln (y)

ln (e^{iπ}) - ln (3 e^{iπ} + 4)

8 lo g_{10} (x) - lo g_{10} (\frac{1}{x}) - lo g_{10} (y)

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