What is log_{b}(x^2y^9z) ?

The solution to log_{b}(x^2y^9z) is 2log_{b}(x)+9log_{b}(y)+log_{b}(z)

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simplify log_{b}(x^2y^9z)

simplify

lo g_{b} (x^{2} y^{9} z)

2 lo g_{b} (x) + 9 lo g_{b} (y) + lo g_{b} (z)

Solution steps

lo g_{b} (x^{2} y^{9} z)

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{b} (x^{2} y^{9} z) = lo g_{b} (x^{2}) + lo g_{b} (y^{9}) + lo g_{b} (z)

= lo g_{b} (x^{2}) + lo g_{b} (y^{9}) + lo g_{b} (z)

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

lo g_{b} (y^{9}) = 9 lo g_{b} (y)

= 2 lo g_{b} (x) + 9 lo g_{b} (y) + lo g_{b} (z)

- lo g_{10} (1 x 1 0^{- 11})

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

lo g_{3} (x) - lo g_{3} (4)

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

lo g_{3} (13 x)

What is log_{b}(x^2y^9z) ?
The solution to log_{b}(x^2y^9z) is 2log_{b}(x)+9log_{b}(y)+log_{b}(z)