5ln(4x−9)+7=−8

Sure, let's solve the equation step by step:

1. First, isolate the natural logarithm term by subtracting 7 from both sides of the equation:

   5ln(4x - 9) = -8 - 7 5ln(4x - 9) = -15

2. Next, divide both sides of the equation by 5 to get the natural logarithm by itself:

   ln(4x - 9) = -15 / 5 ln(4x - 9) = -3

3. Now, to remove the natural logarithm, we can use the property of logarithms that says e^(ln(a)) = a. So, we raise e to the power of both sides of the equation:

   e^(ln(4x - 9)) = e^(-3) 4x - 9 = e^(-3)

4. Add 9 to both sides of the equation to isolate the term with x:

   4x = e^(-3) + 9

5. Finally, divide both sides of the equation by 4 to solve for x:

   x = (e^(-3) + 9) / 4

So, the solution to the equation 5ln(4x - 9) + 7 = -8 is x = (e^(-3) + 9) / 4.