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

The solution to log_{b}(x^3y^2z) is 3log_{b}(x)+2log_{b}(y)+log_{b}(z)

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

simplify

lo g_{b} (x^{3} y^{2} z)

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

Solution steps

lo g_{b} (x^{3} y^{2} z)

Apply log rule:

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

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

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

lo g_{b} (x^{3}) = 3 lo g_{b} (x)

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

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

lo g_{10} (\frac{6 ( 5 + x ) ^{4}}{x ^{2}})

2 ln (3) + ln (2)

lo g_{2} (3 x) + lo g_{2} (4^{4})

\frac{ln ( 6 ) - ln ( 5 )}{4}

ln (\frac{7 x 1 + 6 x}{( x - 4 ) ^{4}})

What is log_{b}(x^3y^2z) ?
The solution to log_{b}(x^3y^2z) is 3log_{b}(x)+2log_{b}(y)+log_{b}(z)