Solve the following: 3ln(4x)=17
3ln(4x) = 17
ln(4x) = 17/3
4x = e^(17/3)
x = (1/4) e^(17/3)
To solve the equation 3ln(4x) = 17, we first need to isolate the natural logarithm term.
Step 1: Divide both sides of the equation by 3:
ln(4x) = 17/3
Step 2: Remove the natural logarithm by taking the exponentiation of both sides using the base e (Euler's number):
e^(ln(4x)) = e^(17/3)
Step 3: Simplify the left side of the equation:
4x = e^(17/3)
Step 4: Divide both sides of the equation by 4 to solve for x:
x = e^(17/3) / 4
So the solution to the equation 3ln(4x) = 17 is x = e^(17/3) / 4.