how do I convert (ln) y= a*b^x to base of e??

I have an equation i have found first of all using the same set of data which is y = 49.65e ^(-0.027x), and i now need to make the following equation match with that one;
ln y = 3.93 x (0.99^x)

do you know want is real math

no

To convert the equation (ln) y = a*b^x to the base of e, you can follow these steps:

Step 1: Convert the exponential term b^x to the base of e.
- Recall the logarithmic identity: ln(x^y) = y * ln(x).
- Apply this identity to the exponential term b^x: ln(b^x) = x * ln(b).
- Since we want to convert to the base of e, replace ln(b) with an equivalent expression, ln(b) = ln(b)/ln(e) = ln(b)/1 = ln(b).
- Substituting back into the equation, we get ln(b^x) = x * ln(b) = x * ln(b).
- Therefore, the equation becomes ln(y) = a * x * ln(b).

Step 2: Simplify the equation.
- Since the equation is ln(y) = a * x * ln(b), we can rearrange it to ln(y) = ln(b) * (a * x).
- The equation is now in the form ln(y) = kx, where k = ln(b) * a.

So, to convert the equation (ln) y = a*b^x to the base of e, you can rewrite it as ln(y) = ln(b) * (a * x).

Now, let's apply this to your specific equation: ln(y) = 3.93 x (0.99^x).

Step 1: Convert the exponential term (0.99^x) to the base of e.
- Apply the logarithmic identity: ln(x^y) = y * ln(x).
- ln(0.99^x) = x * ln(0.99).
- Since we want to convert to the base of e, ln(0.99) = ln(0.99)/ln(e) = ln(0.99)/1 = ln(0.99).
- Substituting back into the equation, we get ln(0.99^x) = x * ln(0.99).

Step 2: Simplify the equation.
- Rearrange the equation to ln(y) = ln(0.99) * 3.93 * x.

So, your equation ln(y) = 3.93 x (0.99^x) can be converted to the base of e as ln(y) = ln(0.99) * 3.93 * x.

Please note that ln(0.99) * 3.93 is a constant value, which can be calculated using a calculator or other computational tools.