What is log_{b}((x^2y)/(z^7)) ?

The solution to log_{b}((x^2y)/(z^7)) is 2log_{b}(x)+log_{b}(y)-7log_{b}(z)

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simplify log_{b}((x^2y)/(z^7))

simplify

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

2 lo g_{b} (x) + lo g_{b} (y) - 7 lo g_{b} (z)

Solution steps

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

Apply log rule:

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

lo g_{b} (\frac{x ^{2} y}{z ^{7}}) = lo g_{b} (x^{2} y) - lo g_{b} (z^{7})

= lo g_{b} (x^{2} y) - lo g_{b} (z^{7})

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

lo g_{b} (z^{7}) = 7 lo g_{b} (z)

= 2 lo g_{b} (x) + lo g_{b} (y) - 7 lo g_{b} (z)

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

lo g_{7} (k^{2} - 49) - lo g_{7} (k - 7)

2 - lo g_{7} (6) - 2 lo g_{7} (x)

lo g_{7} (k^{2} - 49) - lo g_{7} (k) - 7

ln (x - 1) - ln (x + 1)

What is log_{b}((x^2y)/(z^7)) ?
The solution to log_{b}((x^2y)/(z^7)) is 2log_{b}(x)+log_{b}(y)-7log_{b}(z)