How do you do 4ln(2x+3)=11
ln(2x+3)^4 = 11
e^ln(2x+3)^4 = (2x+3)^4 = e^11
(2x+3) = (e^11)^.25 = e^2.75 = 15.64
2x = 12.64
x = 6.32
To solve the equation 4ln(2x+3) = 11, we need to isolate the variable x. Here are the steps to find the solution:
Step 1: Divide both sides of the equation by 4. This gives us:
ln(2x+3) = 11/4
Step 2: Rewrite the equation in its exponential form. The natural logarithm (ln) of a number is the exponent to which e (approximately 2.71828) must be raised to obtain that number. So, the equation can be written as:
2x+3 = e^(11/4)
Step 3: Subtract 3 from both sides of the equation:
2x = e^(11/4) - 3
Step 4: Divide both sides of the equation by 2:
x = (e^(11/4) - 3)/2
Now you have found the solution for x in terms of e. You can use a calculator to find the approximate value for x by plugging in the value of e and evaluating the expression.