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

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

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

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

x = 2 + 3

Decimal Notation

x = 3.73205 \dots

Solution steps

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

Apply log rules

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

Solve

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

x = 2 + 3, x = 2 - 3

Verify Solutions:

x = 2 + 3

True

, x = 2 - 3

False

The solution is

x = 2 + 3

lo g_{x} (625) = 4

ln (6) + ln (x) - ln (2) = 3

lo g_{3} (4 x - 5) = lo g_{3} (2 x + 1)

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

lo g_{2} (x) = 1

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