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

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

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2log_{10}(x-1)=log_{10}(2x+2)

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

x = 2 + 5

Decimal

x = 4.23606 \dots

Solution steps

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

Apply log rules

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

Solve

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

x = 2 + 5, x = 2 - 5

Verify Solutions:

x = 2 + 5

True

, x = 2 - 5

False

The solution is

x = 2 + 5

lo g_{10} (x - 2) + lo g_{10} (12 - x) = 0

lo g_{x} (25) = 4

lo g_{10} (x) = 3

lo g_{2} (4 - x) = 7

ln (x) = 5

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