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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

lo g_{6} (7 x)

lo g_{5} (\frac{25}{y})

ln (x + 1) + ln (x - 1)

lo g_{5} (8) + lo g_{5} (12)

5 lo g_{b} (m) - lo g_{b} (n)

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