What is log_{5}((x^4y^9)/(z^6)) ?

The solution to log_{5}((x^4y^9)/(z^6)) is 4log_{5}(x)+9log_{5}(y)-6log_{5}(z)

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simplify log_{5}((x^4y^9)/(z^6))

simplify

lo g_{5} (\frac{x ^{4} y ^{9}}{z ^{6}})

4 lo g_{5} (x) + 9 lo g_{5} (y) - 6 lo g_{5} (z)

Solution steps

lo g_{5} (\frac{x ^{4} y ^{9}}{z ^{6}})

Apply log rule:

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

lo g_{5} (\frac{x ^{4} y ^{9}}{z ^{6}}) = lo g_{5} (x^{4} y^{9}) - lo g_{5} (z^{6})

= lo g_{5} (x^{4} y^{9}) - lo g_{5} (z^{6})

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

lo g_{5} (z^{6}) = 6 lo g_{5} (z)

= 4 lo g_{5} (x) + 9 lo g_{5} (y) - 6 lo g_{5} (z)

\frac{1}{2} [lo g_{2} (x) + lo g_{2} (x + 1)]

ln (\frac{x ^{2} - x - 2}{( x + 4 ) ^{2}})^{\frac{1}{3}}

\frac{1}{2} ln 2 + 2 v^{2} - \frac{1}{2} arctan (v) + ln (x)

lo g_{7} (3 k)

lo g_{10} (2) + lo g_{10} (4) + lo g_{10} (8)

What is log_{5}((x^4y^9)/(z^6)) ?
The solution to log_{5}((x^4y^9)/(z^6)) is 4log_{5}(x)+9log_{5}(y)-6log_{5}(z)