Answer :
To solve the equation [tex]\( e^{-x+5} - 7 = 16 \)[/tex], we need to isolate [tex]\( x \)[/tex]. Let's break it down into a series of steps:
1. Start with the given equation:
[tex]\[
e^{-x+5} - 7 = 16
\][/tex]
2. Add 7 to both sides to isolate the exponential term:
[tex]\[
e^{-x+5} = 16 + 7
\][/tex]
[tex]\[
e^{-x+5} = 23
\][/tex]
3. Take the natural logarithm (ln) of both sides to solve for the exponent:
[tex]\[
-x + 5 = \ln(23)
\][/tex]
4. Isolate [tex]\( x \)[/tex]:
Subtract 5 from both sides:
[tex]\[
-x = \ln(23) - 5
\][/tex]
Multiply both sides by -1 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 5 - \ln(23)
\][/tex]
So, the solution is:
[tex]\[
x = 5 - \ln(23)
\][/tex]
This provides the value of [tex]\( x \)[/tex] that satisfies the original equation.
1. Start with the given equation:
[tex]\[
e^{-x+5} - 7 = 16
\][/tex]
2. Add 7 to both sides to isolate the exponential term:
[tex]\[
e^{-x+5} = 16 + 7
\][/tex]
[tex]\[
e^{-x+5} = 23
\][/tex]
3. Take the natural logarithm (ln) of both sides to solve for the exponent:
[tex]\[
-x + 5 = \ln(23)
\][/tex]
4. Isolate [tex]\( x \)[/tex]:
Subtract 5 from both sides:
[tex]\[
-x = \ln(23) - 5
\][/tex]
Multiply both sides by -1 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 5 - \ln(23)
\][/tex]
So, the solution is:
[tex]\[
x = 5 - \ln(23)
\][/tex]
This provides the value of [tex]\( x \)[/tex] that satisfies the original equation.
