Question - Solving Exponential Equation for Unknown Variable
mathnatural logarithmsolving exponential equationunknown variableisolate term containing xcalculating ln(9)
Solution:
The equation in the image is $$ e^{x - 7} + 11 = 20 $$. To solve for $$ x $$, we want to isolate the term containing $$ x $$. Here are the steps:1. Subtract 11 from both sides of the equation to get the exponential term by itself: $$ e^{x - 7} = 20 - 11 $$ $$ e^{x - 7} = 9 $$2. Take the natural logarithm (ln) of both sides to 'undo' the exponential. Since $$ \ln(e^y) = y $$, we have: $$ \ln(e^{x - 7}) = \ln(9) $$ $$ x - 7 = \ln(9) $$3. Add 7 to both sides to solve for $$ x $$: $$ x = \ln(9) + 7 $$Now we have the solution for $$ x $$. If a specific numerical value is required, you'd compute $$ \ln(9) $$ using a calculator and then add 7 to that result.
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