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

The solution to log_{10}((x^2y^3)/(yz^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} y ^{3}}{y 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)

ln (25 (0^{2} + 1)^{2})

lo g_{b} (\frac{a y ^{5}}{m ^{3} n ^{4}})

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

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