Question

Given the exponential function y = 7^x, find the inverse equation.

Answer 1

To find the inverse of the exponential function y = 7^x, swap x and y, take the natural logarithm of both sides, use logarithmic properties, and solve for the new y to get the inverse equation y = ln(x) / ln(7).

Step-by-step explanation:

To find the inverse equation of the exponential function y = 7^x, we follow these steps:

1. Replace y with x and vice versa, resulting in x = 7^y.
2. Take the natural logarithm (ln) of both sides to get ln(x) = ln(7^y).
3. Using the property of logarithms that ln(a^b) = b ln(a), we can rewrite the equation as ln(x) = y ln(7).
4. Finally, to solve for y, divide both sides by ln(7) to obtain y = ln(x) / ln(7),

which gives us the inverse equation of y = 7^x.