Question - Solving Exponential Equation with Natural Logarithm
Solution:
The equation in the image is $$ e^x + 11 = 20 $$. To solve for $$ x $$, you want to isolate $$ e^x $$ on one side of the equation. Here are the steps to do that:1. Subtract 11 from both sides of the equation to isolate the exponential term on one side:$$ e^x + 11 - 11 = 20 - 11 $$Simplifying that, you get:$$ e^x = 9 $$2. Taking the natural logarithm (ln) of both sides to solve for $$ x $$:$$ \ln(e^x) = \ln(9) $$Since $$ \ln(e^x) $$ simplifies to $$ x $$(because $$ \ln(e^x) $$ and $$ e^x $$ are inverse functions), you have:$$ x = \ln(9) $$The approximate value of $$ x $$ can be found using a calculator:$$ x \approx \ln(9) \approx 2.1972 $$
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com