What is the answer to 2log_{10}(x)-log_{10}(x-1)=1 ?

The answer to 2log_{10}(x)-log_{10}(x-1)=1 is x=5+sqrt(15),x=5-sqrt(15)

Solve for x: 2log_{10}(x)-log_{10}(x-1)=1

The solution is x=5+sqrt(15),x=5-sqrt(15)

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

x = 5 + 15, x = 5 - 15

Decimal Notation

x = 8.87298 \dots, x = 1.12701 \dots

Solution steps

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

Apply log rules

x^{2} = 10 (x - 1)

Solve

x^{2} = 10 (x - 1) : x = 5 + 15, x = 5 - 15

x = 5 + 15, x = 5 - 15

Verify Solutions:

x = 5 + 15

True

, x = 5 - 15

True

The solutions are

x = 5 + 15, x = 5 - 15

lo g_{e} (x^{2} - 2 x - 2) = 0

ln (\frac{x}{5}) = 4.44

6 = lo g_{2} (5 - 3 x)

5 - 2 ln (x) = 7

lo g_{10} (2 x - 1) = lo g_{10} (13)

What is the answer to 2log_{10}(x)-log_{10}(x-1)=1 ?
The answer to 2log_{10}(x)-log_{10}(x-1)=1 is x=5+sqrt(15),x=5-sqrt(15)
Solve for x: 2log_{10}(x)-log_{10}(x-1)=1
The solution is x=5+sqrt(15),x=5-sqrt(15)