What is log_{b}((sqrt(x))/((yz)^2)) ?

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

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simplify log_{b}((sqrt(x))/((yz)^2))

simplify

lo g_{b} (\frac{x}{( yz ) ^{2}})

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

Solution steps

lo g_{b} (\frac{x}{( yz ) ^{2}})

Simplify

\frac{x}{( yz ) ^{2}} : \frac{x}{y ^{2} z ^{2}}

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

Apply log rule:

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

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

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

Simplify

lo g_{b} (y^{2} z^{2}) : 2 lo g_{b} (y) + 2 lo g_{b} (z)

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

Apply the distributive law:

- (a + b) = - a - b

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

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

- lo g_{10} (3 \cdot 1 0^{- 5})

lo g_{4} (\frac{1}{8}) \cdot lo g_{8} (256)

ln (x + 4) - 3 ln (x) - ln (y)

lo g_{10} (\frac{a c}{b})

lo g_{x} ((a) (4))

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