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

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

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

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

x = - 2 + 3

Decimal Notation

x = - 0.26794 \dots

Solution steps

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

Apply log rules

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

Solve

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

ln (10 x - 25) - 2 ln (x) = 0

lo g_{7} (a) = 3

lo g_{10} (3 y - 1) = 2

lo g_{6} (9 x) = 2

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