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

258

likes1288 views

Santino

4.5

54 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

Frequently asked questions (FAQs)

What is the result of (3^2) * (3^4)?

+

What is the area of a circle with a diameter of 10 cm?

+

What is the median of a set of numbers if the data set has 7 elements?

+

New questions in Mathematics