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

The solution to 3log_{10}(x^3y)+2log_{10}(yz^2) is log_{10}(x^9y^5z^4)

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

simplify

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

lo g_{10} (x^{9} y^{5} z^{4})

Solution steps

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

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

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

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

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

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

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

Simplify

(x^{3} y)^{3} (y z^{2})^{2} : x^{9} y^{5} z^{4}

= lo g_{10} (x^{9} y^{5} z^{4})

2 lo g_{10} (x) - 5 lo g_{10} (x + 1)

lo g_{3} (\frac{x ^{4}}{y ^{\frac{3}{5}}})

lo g_{4} (3) + lo g_{4} (10)

\frac{- 4 ln ( 2 ) - 7 ln ( 7 )}{5 ln ( 7 ) - ln ( 2 )}

ln (\frac{A}{B})

What is 3log_{10}(x^3y)+2log_{10}(yz^2) ?
The solution to 3log_{10}(x^3y)+2log_{10}(yz^2) is log_{10}(x^9y^5z^4)