If Logx - Log(2x - 1)=1 Find X

Please I Need Help. Help Me To Solve The Equation

since loga - logb = log(a/b), we have

log x/(2x-1) = 1
x/(2x-1) = 10^1 = 10
now just find x.

If logx

X=19/10

To solve the equation Log(x) - Log(2x - 1) = 1 and find the value of x, we can use the properties of logarithms. By applying the quotient rule of logarithms, which states that Log(a) - Log(b) = Log(a/b), we can rewrite the equation as:

Log(x / (2x - 1)) = 1

Now, we can convert the logarithmic equation into an exponential equation. Recall that Log(a) = b can be rewritten as a = 10^b. Applying this rule, we have:

x / (2x - 1) = 10^1

Simplifying the right side of the equation gives:

x / (2x - 1) = 10

Next, we can cross-multiply to solve for x:

x = 10(2x - 1)

Expanding the right side of the equation:

x = 20x - 10

To isolate x, we can move the terms without x to the right side:

x - 20x = -10

Combining like terms:

-19x = -10

Dividing both sides by -19 gives:

x = -10 / -19

Now, divide -10 by -19 using a calculator or long division:

x ≈ 0.526

Therefore, the approximate value of x that satisfies the equation Log(x) - Log(2x - 1) = 1 is approximately 0.526.