log3 x-log3(1-x)=3
remember
log a - log b= log (a/b)
so log (x/(1-x))=3
take the antilog of each side.
x/(1-x)=1000
solve for x
To solve the equation log3(x) - log3(1-x) = 3, we first need to use the properties of logarithms to simplify the equation.
Using the property of logarithms that states log(a) - log(b) = log(a/b), we can rewrite the equation as:
log3(x / (1-x)) = 3
Next, we need to convert the logarithmic equation into an exponential equation. In general, if loga(b) = c, then a^c = b.
Applying this to our equation, we have:
3^(log3(x / (1-x))) = 3^3
Simplifying the right side, we get:
x / (1-x) = 27
Now, we can solve for x by multiplying both sides of the equation by (1-x):
x = 27(1-x)
Expanding the right side:
x = 27 - 27x
Moving all the x terms to one side:
x + 27x = 27
Combining like terms:
28x = 27
Finally, solving for x by dividing both sides by 28:
x = 27 / 28