Sure, let's solve the exponential equation step by step:
Given the equation:
[tex]\[ -18 + 3e^x = 18 \][/tex]
1. Isolate the exponential term:
[tex]\[ -18 + 3e^x = 18 \][/tex]
Add 18 to both sides:
[tex]\[ 3e^x = 18 + 18 \][/tex]
[tex]\[ 3e^x = 36 \][/tex]
2. Solve for [tex]\( e^x \)[/tex]:
Divide both sides by 3:
[tex]\[ e^x = \frac{36}{3} \][/tex]
[tex]\[ e^x = 12 \][/tex]
3. Take the natural logarithm of both sides to solve for [tex]\( x \)[/tex]:
[tex]\[ \ln(e^x) = \ln(12) \][/tex]
Using the property of logarithms that [tex]\( \ln(e^x) = x \)[/tex], we have:
[tex]\[ x = \ln(12) \][/tex]
Thus, the solution to the given exponential equation is:
[tex]\[ x = \ln(12) \][/tex]
