What is the answer to 2log_{10}(x-1)-log_{10}(x)=0 ?

The answer to 2log_{10}(x-1)-log_{10}(x)=0 is x=(3+sqrt(5))/2

Solve for x: 2log_{10}(x-1)-log_{10}(x)=0

The solution is x=(3+sqrt(5))/2

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2 lo g_{10} (x - 1) - lo g_{10} (x) = 0

x = \frac{3 + 5}{2}

Decimal Notation

x = 2.61803 \dots

Solution steps

2 lo g_{10} (x - 1) - lo g_{10} (x) = 0

Apply log rules

(x - 1)^{2} = x

Solve

(x - 1)^{2} = x : x = \frac{3 + 5}{2}, x = \frac{3 - 5}{2}

x = \frac{3 + 5}{2}, x = \frac{3 - 5}{2}

Verify Solutions:

x = \frac{3 + 5}{2}

True

, x = \frac{3 - 5}{2}

False

The solution is

x = \frac{3 + 5}{2}

lo g_{2} (4 x - 1) = 3

x, y = ln (x y)

ln (1 - 2 x) = 0.4

lo g_{10} (x^{3} + 2000) = 2

ln (x + 4) - ln (x - 6) = 1

What is the answer to 2log_{10}(x-1)-log_{10}(x)=0 ?
The answer to 2log_{10}(x-1)-log_{10}(x)=0 is x=(3+sqrt(5))/2
Solve for x: 2log_{10}(x-1)-log_{10}(x)=0
The solution is x=(3+sqrt(5))/2