What is 2log_{5}(X+1)-log_{5}(X-1) ?

The solution to 2log_{5}(X+1)-log_{5}(X-1) is log_{5}(((X+1)^2)/(X-1))

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simplify 2log_{5}(X+1)-log_{5}(X-1)

simplify

2 lo g_{5} (X + 1) - lo g_{5} (X - 1)

lo g_{5} (\frac{( X + 1 ) ^{2}}{X - 1})

Solution steps

2 lo g_{5} (X + 1) - lo g_{5} (X - 1)

Apply log rule:

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

2 lo g_{5} (X + 1) = lo g_{5} ((X + 1)^{2})

= lo g_{5} ((X + 1)^{2}) - lo g_{5} (X - 1)

Apply log rule:

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

lo g_{5} ((X + 1)^{2}) - lo g_{5} (X - 1) = lo g_{5} (\frac{( X + 1 ) ^{2}}{X - 1})

= lo g_{5} (\frac{( X + 1 ) ^{2}}{X - 1})

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

ln (\frac{13}{20})

ln (\frac{7 x}{x ^{2} + 7})

ln (y) - ln (x) - ln (c)

112 + 96 ln (2) - 75 ln (5)

What is 2log_{5}(X+1)-log_{5}(X-1) ?
The solution to 2log_{5}(X+1)-log_{5}(X-1) is log_{5}(((X+1)^2)/(X-1))