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

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

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

simplify

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

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

Solution steps

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

Simplify

\frac{y ^{3}}{y} : y^{2}

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

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

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

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

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

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

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

\frac{ln ( 5 ) - ln ( 4 )}{ln ( 3 ) - ln ( 2 )}

lo g_{4} (\frac{1}{16} x)

ln (\frac{25}{7})

ln (\frac{8}{3 x ^{3} y})

lo g_{\frac{1}{2}} (\frac{7}{12})

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