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Solve for [tex] x [/tex].

[tex] e^{-x+5} - 7 = 16 [/tex]

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.

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Rewritten by : Barada