Isolate Exponential Term: Step Title: Isolate the Exponential Term Concise Step Description: Add e^(x-8) to both sides to isolate the exponential term on one side of the equation. Step Calculation: 4 + e^(x-8) = 15-e^(x-8) + e^(x-8) Step Output: 4 + e^(x-8) = 15Subtract 4: Step Title: Subtract 4 from Both Sides Concise Step Description: Subtract 4 from both sides to get the exponential term by itself. Step Calculation: 4 + e^(x-8) - 4 = 15 - 4 Step Output: e^(x-8) = 11Take Natural Logarithm: Step Title: Take the Natural Logarithm of Both Sides Concise Step Description: Apply the natural logarithm to both sides to solve for x. Step Calculation: ln(e^(x-8)) = ln(11) Step Output: x - 8 = ln(11)Add 8: Step Title: Add 8 to Both Sides Concise Step Description: Add 8 to both sides to solve for x. Step Calculation: x - 8 + 8 = ln(11) + 8 Step Output: x = ln(11) + 8

Algebra 2

Factor polynomials

Full solution

4=15-e^{x-8}

Isolate Exponential Term: Step Title: Isolate the Exponential Term $\newline$ Concise Step Description: Add $e^{(x-8)}$ to both sides to isolate the exponential term on one side of the equation. $\newline$ Step Calculation: $4 + e^{(x-8)} = 15-e^{(x-8)} + e^{(x-8)}$ $\newline$ Step Output: $4 + e^{(x-8)} = 15$
Subtract $4$ : Step Title: Subtract $4$ from Both Sides $\newline$ Concise Step Description: Subtract $4$ from both sides to get the exponential term by itself. $\newline$ Step Calculation: $4 + e^{(x-8)} - 4 = 15 - 4$ $\newline$ Step Output: $e^{(x-8)} = 11$
Take Natural Logarithm: Step Title: Take the Natural Logarithm of Both Sides $\newline$ Concise Step Description: Apply the natural logarithm to both sides to solve for $x$ . $\newline$ Step Calculation: $\ln(e^{(x-8)}) = \ln(11)$ $\newline$ Step Output: $x - 8 = \ln(11)$
Add $8$ : Step Title: Add $8$ to Both Sides $\newline$ Concise Step Description: Add $8$ to both sides to solve for $x$ . $\newline$ Step Calculation: $x - 8 + 8 = \ln(11) + 8$ $\newline$ Step Output: $x = \ln(11) + 8$