What is log_{5}(x)+2log_{5}(y)-1/2 log_{5}(17) ?

The solution to log_{5}(x)+2log_{5}(y)-1/2 log_{5}(17) is log_{5}((sqrt(17)xy^2)/(17))

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simplify log_{5}(x)+2log_{5}(y)-1/2 log_{5}(17)

simplify

lo g_{5} (x) + 2 lo g_{5} (y) - \frac{1}{2} lo g_{5} (17)

lo g_{5} (\frac{17 x y ^{2}}{17})

Solution steps

lo g_{5} (x) + 2 lo g_{5} (y) - \frac{1}{2} lo g_{5} (17)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= lo g_{5} (x) + lo g_{5} (y^{2}) - \frac{1}{2} lo g_{5} (17)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

= lo g_{5} (x y^{2}) - \frac{1}{2} lo g_{5} (17)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} lo g_{5} (17) = lo g_{5} (1 7^{\frac{1}{2}})

= lo g_{5} (x y^{2}) - lo g_{5} (1 7^{\frac{1}{2}})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{5} (x y^{2}) - lo g_{5} (1 7^{\frac{1}{2}}) = lo g_{5} (\frac{x y ^{2}}{1 7 ^{\frac{1}{2}}})

= lo g_{5} (\frac{x y ^{2}}{1 7 ^{\frac{1}{2}}})

Simplify

\frac{x y ^{2}}{1 7 ^{\frac{1}{2}}} : \frac{17 x y ^{2}}{17}

= lo g_{5} (\frac{17 x y ^{2}}{17})

lo g_{10} (a b^{x})

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

3 ln (\frac{5}{3})

ln (6) + ln (x)

75 - 35 + 10 lo g_{10} (\frac{301}{67.2})

What is log_{5}(x)+2log_{5}(y)-1/2 log_{5}(17) ?
The solution to log_{5}(x)+2log_{5}(y)-1/2 log_{5}(17) is log_{5}((sqrt(17)xy^2)/(17))