What is the answer to log_{5}(x+1)-log_{5}(x-1)=2 ?

The answer to log_{5}(x+1)-log_{5}(x-1)=2 is x= 13/12

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log_{5}(x+1)-log_{5}(x-1)=2

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

x = \frac{13}{12}

Decimal Notation

x = 1.08333 \dots

Solution steps

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

Add

lo g_{5} (x - 1)

to both sides

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

Simplify

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

Apply log rules

x + 1 = 25 (x - 1)

Solve

x + 1 = 25 (x - 1) : x = \frac{13}{12}

x = \frac{13}{12}

Verify Solutions:

x = \frac{13}{12}

True

The solution is

x = \frac{13}{12}

ln (5 x - 1) = 3

lo g_{10} (3) + lo g_{10} (1 - 3 x) = 0

lo g_{6} (x) = 3

lo g_{3} (x) = 1

- lo g_{10} (x) = 2.3

What is the answer to log_{5}(x+1)-log_{5}(x-1)=2 ?
The answer to log_{5}(x+1)-log_{5}(x-1)=2 is x= 13/12
Solve for x: log_{5}(x+1)-log_{5}(x-1)=2
The solution is x= 13/12