Question

Find the inverse of the equation: N = 15 + 6ln(d)

a) N = e^(15+6ln(d))
b) N = 15 - 6ln(d)
c) N = e^(15-6ln(d))
d) N = 15/e^(6ln(d))

Answer 1

To find the inverse of the equation N = 15 + 6ln(d), subtract 15 from both sides and divide by 6 to isolate the logarithmic term. Then, take the inverse of the natural logarithm function by raising e to the power of both sides. The inverse of the equation is N = e^(15+6ln(d)).

Step-by-step explanation:

To find the inverse of the equation N = 15 + 6ln(d), we need to interchange the roles of N and d and solve for N. In this case, N is the dependent variable and d is the independent variable.

Step 1: Start with the equation N = 15 + 6ln(d).

Step 2: Subtract 15 from both sides to isolate the logarithmic term: N - 15 = 6ln(d).

Step 3: Divide both sides by 6 to solve for ln(d): (N - 15)/6 = ln(d).

Step 4: Take the inverse of the natural logarithm function by raising e to the power of both sides: N = e^((N - 15)/6).

Therefore, the inverse of the equation N = 15 + 6ln(d) is option a) N = e^(15+6ln(d)).