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

The answer to log_{x}(2x-1)=-1 is No Solution for x\in\mathbb{R}

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

The solution is No Solution for x\in\mathbb{R}

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

No Solution for x \in R

Solution steps

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

Apply log rules

\frac{ln ( 2 x - 1 )}{ln ( x )} = - 1

Multiply both sides by

ln (x)

\frac{ln ( 2 x - 1 )}{ln ( x )} ln (x) = - 1 \cdot ln (x)

Simplify

ln (2 x - 1) = - ln (x)

Add

ln (x)

to both sides

ln (2 x - 1) + ln (x) = - ln (x) + ln (x)

Simplify

ln (2 x - 1) + ln (x) = 0

Apply log rules

(2 x - 1) x = 1

Solve

(2 x - 1) x = 1 : x = 1, x = - \frac{1}{2}

x = 1, x = - \frac{1}{2}

Verify Solutions:

x = 1

False

, x = - \frac{1}{2}

False

The solution is

No Solution for x \in R

lo g_{10} (x) - 2 lo g_{10} (5 x) = 2

- lo g_{6} (8 w) = 0

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

x^{1 + l o g_{5} (x)} = 25 x^{2}

lo g_{10} (x + 3) = 1 - lo g_{10} (x)

What is the answer to log_{x}(2x-1)=-1 ?
The answer to log_{x}(2x-1)=-1 is No Solution for x\in\mathbb{R}
Solve for x: log_{x}(2x-1)=-1
The solution is No Solution for x\in\mathbb{R}