What is log_{7}((sqrt(7x^9))/y) ?

The solution to log_{7}((sqrt(7x^9))/y) is (1+9log_{7}(x))/2-log_{7}(y)

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simplify log_{7}((sqrt(7x^9))/y)

simplify

lo g_{7} (\frac{7 x ^{9}}{y})

\frac{1 + 9 lo g _{7} ( x )}{2} - lo g_{7} (y)

Solution steps

lo g_{7} (\frac{7 x ^{9}}{y})

Apply log rule:

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

lo g_{7} (\frac{7 x ^{9}}{y}) = lo g_{7} (7 x^{9}) - lo g_{7} (y)

= lo g_{7} (7 x^{9}) - lo g_{7} (y)

Simplify

lo g_{7} (7 x^{9}) : \frac{1 + 9 lo g _{7} ( x )}{2}

= \frac{1 + 9 lo g _{7} ( x )}{2} - lo g_{7} (y)

lo g_{4} (8) + 2 lo g_{4} (3)

lo g_{10} (\frac{2 x}{y})

- lo g_{10} (6.2 \cdot 1 0^{- 10})

lo g_{4} (x^{5}) - lo g_{4} (x^{3})

3 ln (x) - \frac{2}{3} ln (x + 1) + ln (y) - 3 ln (z)

What is log_{7}((sqrt(7x^9))/y) ?
The solution to log_{7}((sqrt(7x^9))/y) is (1+9log_{7}(x))/2-log_{7}(y)