What is log_{5}((sqrt(5x^7))/y) ?

The solution to log_{5}((sqrt(5x^7))/y) is (1+7log_{5}(x))/2-log_{5}(y)

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simplify log_{5}((sqrt(5x^7))/y)

simplify

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

\frac{1 + 7 lo g _{5} ( x )}{2} - lo g_{5} (y)

Solution steps

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

Apply log rule:

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

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

= lo g_{5} (5 x^{7}) - lo g_{5} (y)

Simplify

lo g_{5} (5 x^{7}) : \frac{1 + 7 lo g _{5} ( x )}{2}

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

lo g_{2} (\frac{y}{a})

lo g_{3} (x + 2) + lo g_{3} (x - 4)

7 lo g_{2} (a) + lo g_{2} (6) - lo g_{2} (b)

ln (2) + \frac{1}{2} ln (x + 1) - 2 ln (1 + x)

ln (z) - ln (4 y)

What is log_{5}((sqrt(5x^7))/y) ?
The solution to log_{5}((sqrt(5x^7))/y) is (1+7log_{5}(x))/2-log_{5}(y)