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

The answer to log_{5}(x+5)-log_{5}(x-1)=2 is x= 5/4

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

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

x = \frac{5}{4}

Decimal Notation

x = 1.25

Solution steps

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

Add

lo g_{5} (x - 1)

to both sides

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

Simplify

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

Apply log rules

x + 5 = 25 (x - 1)

Solve

x + 5 = 25 (x - 1) : x = \frac{5}{4}

x = \frac{5}{4}

Verify Solutions:

x = \frac{5}{4}

True

The solution is

x = \frac{5}{4}

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

lo g_{2 x + 1} (2 x^{2} + 10 x - 3) = 2

lo g_{7} (x - 3) + lo g_{7} (x + 3) = 1

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

lo g_{2} (lo g_{5} (x)) = 2

What is the answer to log_{5}(x+5)-log_{5}(x-1)=2 ?
The answer to log_{5}(x+5)-log_{5}(x-1)=2 is x= 5/4
Solve for x: log_{5}(x+5)-log_{5}(x-1)=2
The solution is x= 5/4