Solve for x.
ln x - 2 ln x = ln 64
lnx - ln x^2 = ln 64
ln (x/x^2) = ln 64
x/x^2 = 64
1/x = 64
x = 64
1/64
To solve for x in the equation ln x - 2 ln x = ln 64, we can use the properties of logarithms.
First, let's simplify the left side of the equation using the property: ln(a) - ln(b) = ln(a/b).
ln x - 2 ln x = ln(x) - ln(x^2) = ln(x / x^2) = ln(1 / x)
So, our equation becomes ln(1 / x) = ln 64.
Now, we can use another property of logarithms: ln(a) = ln(b) if and only if a = b.
From ln(1 / x) = ln 64, we know that 1 / x = 64.
To solve for x, we can take the reciprocal of both sides: x = 1 / 64.
Therefore, x = 1 / 64 is the solution to the equation ln x - 2 ln x = ln 64.