What is 1/2 log_{7}(x)-log_{7}(x+1) ?

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

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simplify 1/2 log_{7}(x)-log_{7}(x+1)

simplify

\frac{1}{2} lo g_{7} (x) - lo g_{7} (x + 1)

lo g_{7} (\frac{x ^{\frac{1}{2}}}{x + 1})

Solution steps

\frac{1}{2} lo g_{7} (x) - lo g_{7} (x + 1)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

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

ln (\frac{2 x}{x + 3})

\frac{1}{4} [5 lo g_{10} (x) + lo g_{10} (y)]

lo g_{z} (5 z (z - 5)^{5})

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