What is the answer to log_{6}(x)-log_{6}(x-1)=2 ?

The answer to log_{6}(x)-log_{6}(x-1)=2 is x= 36/35

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log_{6}(x)-log_{6}(x-1)=2

lo g_{6} (x) - lo g_{6} (x - 1) = 2

x = \frac{36}{35}

Decimal Notation

x = 1.02857 \dots

Solution steps

lo g_{6} (x) - lo g_{6} (x - 1) = 2

Add

lo g_{6} (x - 1)

to both sides

lo g_{6} (x) - lo g_{6} (x - 1) + lo g_{6} (x - 1) = 2 + lo g_{6} (x - 1)

Simplify

lo g_{6} (x) = 2 + lo g_{6} (x - 1)

Apply log rules

x = 36 (x - 1)

Solve

x = 36 (x - 1) : x = \frac{36}{35}

x = \frac{36}{35}

Verify Solutions:

x = \frac{36}{35}

True

The solution is

x = \frac{36}{35}

lo g_{2} (x + 4) = 0

lo g_{2} (x + 4) = 4

lo g_{9} (x + 2) - lo g_{9} (x - 6) = 1

x, ln (x^{2} + y) = 0

lo g_{10} (x) = 0.12

What is the answer to log_{6}(x)-log_{6}(x-1)=2 ?
The answer to log_{6}(x)-log_{6}(x-1)=2 is x= 36/35
Solve for x: log_{6}(x)-log_{6}(x-1)=2
The solution is x= 36/35