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

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

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

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

x = \frac{5}{4}

Decimal Notation

x = 1.25

Solution steps

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

Add

lo g_{5} (x - 1)

to both sides

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

Simplify

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

Apply log rules

x = 5 (x - 1)

Solve

x = 5 (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_{6} (x + 4) = 1 - lo g_{6} (x + 3)

lo g_{4} (x) = lo g_{x} (16)

3 ln (5 x + 1) - 8 = 44

ln (x + 1) = ln (x) + ln (1)

lo g_{3} (x - 7) = 4

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