Use logarithms to solve. (If there is no solution, enter NO SOLUTION.)
\[
e^{r+5}-5=-31
\]
Final Answer: \(\boxed{\text{NO SOLUTION}}\)
Step 1 :Given the equation \(e^{r+5}-5=-31\)
Step 2 :Add 5 to both sides of the equation to isolate the exponential term, resulting in \(e^{r+5}=-26\)
Step 3 :Take the natural logarithm (ln) of both sides of the equation to get rid of the exponential term on the left side, resulting in \(r+5=\ln(-26)\)
Step 4 :Subtract 5 from both sides to solve for r, resulting in \(r=\ln(-26)-5\)
Step 5 :However, the natural logarithm of a negative number is undefined in the real number domain, which means that there is no real solution to the equation.
Step 6 :Final Answer: \(\boxed{\text{NO SOLUTION}}\)