What is log_{b}((x^4y^3)/(sqrt(z))) ?

The solution to log_{b}((x^4y^3)/(sqrt(z))) is 4log_{b}(x)+3log_{b}(y)-log_{b}(sqrt(z))

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simplify log_{b}((x^4y^3)/(sqrt(z)))

simplify

lo g_{b} (\frac{x ^{4} y ^{3}}{z})

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

Solution steps

lo g_{b} (\frac{x ^{4} y ^{3}}{z})

Apply log rule:

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

lo g_{b} (\frac{x ^{4} y ^{3}}{z}) = lo g_{b} (x^{4} y^{3}) - lo g_{b} (z)

= lo g_{b} (x^{4} y^{3}) - lo g_{b} (z)

Simplify

lo g_{b} (x^{4} y^{3}) : 4 lo g_{b} (x) + 3 lo g_{b} (y)

= 4 lo g_{b} (x) + 3 lo g_{b} (y) - lo g_{b} (z)

ln (\frac{15}{2})

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

ln (2) \cdot \frac{1}{2}

ln ((x y)^{4})

lo g_{10} (\frac{y}{z ^{4}})

What is log_{b}((x^4y^3)/(sqrt(z))) ?
The solution to log_{b}((x^4y^3)/(sqrt(z))) is 4log_{b}(x)+3log_{b}(y)-log_{b}(sqrt(z))