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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

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

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

lo g_{3} (\frac{81}{x ^{2} + 5})

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

ln (r e^{i θ})

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