Question

Solve for x: 3ex + 2 = 74. Describe the process used to solve the equation and show each step.

Answer 1

The solution of the equation is x = 3.18

Step-by-step explanation:

The equation we have to solve is:

$3e^x + 2 = 74$

First of all, we subtract -2 on both sides of the equation:

$3e^x +2 -2 = 74-2\\3e^x = 72$

Now we divide both sides of the equation by 3:

$\frac{3e^x}{3}=\frac{72}{3}\\e^x=24$

And now we apply the natural logarithm on both sides:

$ln(e^x) = ln(24)\\x=ln(24)$

And using a calculator, we find

$x=ln(24)=3.18$

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