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

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

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

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

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

x = 5 + 15, x = 5 - 15

Decimal Notation

x = 8.87298 \dots, x = 1.12701 \dots

Solution steps

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

Apply log rules

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

Solve

x^{2} = (x - 1) \cdot 10 : 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_{10} (x) = 3.22

lo g_{x} (9) = 2

3 - ln (x) = 3

lo g_{2} (x) = - 3

lo g_{2} (x) = lo g_{4} (x + 6)

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