Question

Solve the following equation for x in exact form and then find the value to the nearest hundredths (make sure to show your work): 5e3x – 3 = 25

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Santino

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91 Answers

To solve the equation 5e^(3x) - 3 = 25 for x, we first add 3 to both sides of the equation to get:
5e^(3x) = 28
Next, we divide both sides by 5 to isolate e^(3x):
e^(3x) = 28/5
To solve for x, we take the natural logarithm of both sides of the equation:
ln(e^(3x)) = ln(28/5)
Using the property of logarithms that ln(e^a) = a, we can simplify the left side of the equation:
3x = ln(28/5)
Finally, we divide both sides by 3 to solve for x:
x = (1/3)ln(28/5)
Using a calculator, we can evaluate this expression to two decimal places:
x ≈ 0.77
Therefore, the solution to the equation 5e^(3x) - 3 = 25 is x ≈ 0.77

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