: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve ln2+lnx=5
. Round to the nearest thousandth, if necessary.
To solve the equation ln2 + lnx = 5, we can combine the logarithms by using the properties of logarithms.
ln2 + lnx = 5
ln(2x) = 5
To solve for x, we can rewrite the equation in exponential form:
e^5 = 2x
x = e^5 / 2
Now, let's calculate the value of x:
x ≈ e^5 / 2
x ≈ 148.413 / 2
x ≈ 74.207
Therefore, the solution to the equation ln2 + lnx = 5 is x ≈ 74.207.