Question

1. solve the following equation using logarithms:

$5e^{x-3}-4=11$
$x=6$
$x=4.099$
$x=1.099$
$x=0.477$
clear all

Explanation:

Step1: Isolate the exponential term

$5e^{x-3} = 11 + 4$
$5e^{x-3} = 15$

Step2: Simplify the equation

$e^{x-3} = \frac{15}{5}$
$e^{x-3} = 3$

Step3: Take natural log of both sides

$\ln(e^{x-3}) = \ln(3)$
$x-3 = \ln(3)$

Step4: Solve for x

$x = \ln(3) + 3$
$x \approx 1.0986 + 3 = 4.0986 \approx 4.099$

Answer:

x = 4.099