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

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

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

simplify

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

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

Solution steps

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

Simplify

x^{3} \frac{y ^{2}}{z} : \frac{x ^{3} y}{z}

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

Apply log rule:

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

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

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

Simplify

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

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

ln (\frac{4 x}{7 y ^{2}})

lo g_{5} (\frac{25 b ^{5} y ^{2} - 6}{y ( x + 6 ) ^{2}})

lo g_{2} (\frac{p ^{5}}{q ^{9}})

- lo g_{10} (6.5 \cdot 1 0^{- 6})

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