Solve for x using the laws of logarithms.
ln(ln x)= 1
take the anti log of each side.
lnx=e
take the antilog of each side
x= e^e
To solve for x in the equation ln(ln x) = 1 using the laws of logarithms, follow the steps below:
Step 1: Exponentiate both sides of the equation using the base of natural logarithm, e. This will eliminate the ln in the equation, leading to:
e^ln(ln x) = e^1.
Step 2: Since e^ln a = a for any positive real number a, the left side simplifies to:
ln x = e.
Step 3: To remove the ln from x on the left side, apply the inverse operation, which is exponentiation with base e, to both sides of the equation:
e^(ln x) = e^e.
Step 4: As a result of applying the inverse operation, the left side becomes:
x = e^e.
Therefore, the solution for x is x = e^e (approximately 15.1542).