What is 2log_{5}(x)-log_{5}(y)-1/2 log_{5}(z) ?

The solution to 2log_{5}(x)-log_{5}(y)-1/2 log_{5}(z) is log_{5}((x^2)/(ysqrt(z)))

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simplify 2log_{5}(x)-log_{5}(y)-1/2 log_{5}(z)

simplify

2 lo g_{5} (x) - lo g_{5} (y) - \frac{1}{2} lo g_{5} (z)

lo g_{5} (\frac{x ^{2}}{y z})

Solution steps

2 lo g_{5} (x) - lo g_{5} (y) - \frac{1}{2} lo g_{5} (z)

2 lo g_{5} (x) = lo g_{5} (x^{2})

- \frac{1}{2} lo g_{5} (z) = - lo g_{5} (z^{\frac{1}{2}})

= lo g_{5} (x^{2}) - lo g_{5} (y) - lo g_{5} (z^{\frac{1}{2}})

Apply log rule:

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

lo g_{5} (x^{2}) - lo g_{5} (y) = lo g_{5} (\frac{x ^{2}}{y})

= lo g_{5} (\frac{x ^{2}}{y}) - lo g_{5} (z^{\frac{1}{2}})

Apply log rule:

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

lo g_{5} (\frac{x ^{2}}{y}) - lo g_{5} (z^{\frac{1}{2}}) = lo g_{5} (\frac{\frac{x ^{2}}{y}}{z ^{\frac{1}{2}}})

= lo g_{5} (\frac{\frac{x ^{2}}{y}}{z ^{\frac{1}{2}}})

Simplify

\frac{\frac{x ^{2}}{y}}{z ^{\frac{1}{2}}} : \frac{x ^{2}}{y z ^{\frac{1}{2}}}

= lo g_{5} (\frac{x ^{2}}{y z ^{\frac{1}{2}}})

Apply exponent rule:

a^{\frac{1}{2}} = a

z^{\frac{1}{2}} = z

= lo g_{5} (\frac{x ^{2}}{y z})

lo g_{10} (\frac{1000 c ^{5}}{2 d ^{4}})

lo g_{2} (2000) - lo g_{2} (150)

lo g_{5} (4) + lo g_{5} (6)

lo g_{9} (Y) + 5 lo g_{9} (U) + \frac{2 lo g _{9} ( O )}{3}

lo g_{10} (5 x^{4} y)

What is 2log_{5}(x)-log_{5}(y)-1/2 log_{5}(z) ?
The solution to 2log_{5}(x)-log_{5}(y)-1/2 log_{5}(z) is log_{5}((x^2)/(ysqrt(z)))