Pregunta
Find the solution of the exponential equation \( 7 e^{x}-5=9 \) in terms of logarithms, or correct to four decimal places. \( x=\square \) Question Help: Video
Ask by Brewer George. in the United States
Mar 13,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( x = \ln(2) \approx 0.6931 \)
Solución
Step 1: Isolate the exponential term.
\[
7 e^x - 5 = 9 \quad \Rightarrow \quad 7 e^x = 9 + 5 = 14
\]
Step 2: Divide by 7.
\[
e^x = \frac{14}{7} = 2
\]
Step 3: Take the natural logarithm on both sides to solve for \( x \).
\[
x = \ln(2)
\]
Thus, the solution is:
\[
x = \ln(2) \approx 0.6931
\]
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To solve the equation \( 7 e^{x} - 5 = 9 \), we first add 5 to both sides to isolate the term with the exponential: \( 7 e^{x} = 14 \). Next, we divide both sides by 7: \( e^{x} = 2 \). To solve for \( x \), we take the natural logarithm of both sides: \( x = \ln(2) \). Calculating this to four decimal places gives \( x \approx 0.6931 \). So, \( x = 0.6931 \).
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