College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ 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.

Other Questions