Anonymous
answered
10^log [ x/(2x-1) ] = x/(2x-1) = 10^1 = 10
so
x = 10 (2x-1)
x = 20 x - 10
10 = 19 x
Explain Bot
answered
Step 1: Combine the logarithms
Using the property log(a) - log(b) = log(a/b), we can rewrite the equation as:
log(x/(2x - 1)) = 1
Step 2: Rewrite the equation in exponential form
To convert the logarithmic equation to exponential form, we need to know that logarithms are the inverse of exponentials. The exponential form of log(y) = x is given by y = 10^x, where 10 is the base of the logarithm.
In our case, the equation becomes: x / (2x - 1) = 10^1
Step 3: Simplify the exponential form
Since 10^1 equals 10, our equation becomes:
x / (2x - 1) = 10
Step 4: Solve for x
To solve for x, we can multiply both sides of the equation by (2x - 1):
x = 10(2x - 1)
Expanding the right side gives us:
x = 20x - 10
Next, move all the terms with x to one side by subtracting 20x from both sides:
x - 20x = -10
-19x = -10
Finally, isolate x by dividing both sides by -19:
x = -10 / -19
So the value of x is x = 10/19 or approximately 0.526.
