What is log_{5}((x^2)/(y^2z^3)) ?

The solution to log_{5}((x^2)/(y^2z^3)) is 2log_{5}(x)-2log_{5}(y)-3log_{5}(z)

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simplify log_{5}((x^2)/(y^2z^3))

simplify

lo g_{5} (\frac{x ^{2}}{y ^{2} z ^{3}})

2 lo g_{5} (x) - 2 lo g_{5} (y) - 3 lo g_{5} (z)

Solution steps

lo g_{5} (\frac{x ^{2}}{y ^{2} z ^{3}})

Apply log rule:

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

lo g_{5} (\frac{x ^{2}}{y ^{2} z ^{3}}) = lo g_{5} (x^{2}) - lo g_{5} (y^{2} z^{3})

= lo g_{5} (x^{2}) - lo g_{5} (y^{2} z^{3})

lo g_{5} (x^{2}) = 2 lo g_{5} (x)

lo g_{5} (y^{2} z^{3}) = 2 lo g_{5} (y) + 3 lo g_{5} (z)

= 2 lo g_{5} (x) - (2 lo g_{5} (y) + 3 lo g_{5} (z))

Apply the distributive law:

- (a + b) = - a - b

- (2 lo g_{5} (y) + 3 lo g_{5} (z)) = - 2 lo g_{5} (y) - 3 lo g_{5} (z)

= 2 lo g_{5} (x) - 2 lo g_{5} (y) - 3 lo g_{5} (z)

lo g_{10} (\frac{7 x}{y ^{2}})

8 ln (x) - \frac{1}{6} ln (y)

lo g_{4} (\frac{x - 4}{y ^{2} ( 5 z )})

lo g_{7} (\frac{49 b ^{7} y ^{2} - 9}{y ( x + 9 ) ^{2}})

lo g_{7} (x) - lo g_{7} (x^{11})

What is log_{5}((x^2)/(y^2z^3)) ?
The solution to log_{5}((x^2)/(y^2z^3)) is 2log_{5}(x)-2log_{5}(y)-3log_{5}(z)