Solve equation. -6e^8n+8 -3=-23

do you mean (8n+8) ?????

To solve the equation -6e^8n + 8 - 3 = -23, let's break it down step by step.

Step 1: Combine like terms.
Start by combining the constants on both sides of the equation:
-6e^8n + 8 - 3 = -23
-6e^8n + 5 = -23

Step 2: Move the constant to the other side of the equation.
To do this, subtract 5 from both sides of the equation:
-6e^8n + 5 - 5 = -23 - 5
-6e^8n = -28

Step 3: Isolate the exponential term.
To do this, divide both sides of the equation by -6:
(-6e^8n)/-6 = -28/-6
e^8n = 28/6

Step 4: Take the natural logarithm on both sides.
Applying the natural logarithm (ln) function to both sides of the equation helps us solve for n:
ln(e^8n) = ln(28/6)
8n = ln(28/6)

Step 5: Solve for n.
Divide both sides of the equation by 8:
(8n)/8 = ln(28/6)/8
n = ln(28/6)/8

Thus, the solution to the equation -6e^8n + 8 - 3 = -23 is n = ln(28/6)/8.