Question

What value of x makes the equation 5e³ˣ=33 true?

Answer 1

To find the value of x that makes the equation 5e³ˣ=33 true, we use logarithms to solve for x. The value of x is approximately x = 0.453.

Step-by-step explanation:

To find the value of x that makes the equation 5e³ˣ=33 true, we can use logarithms.

1. Start by taking the natural logarithm of both sides of the equation: ln(5e³ˣ) = ln(33).
2. Apply the logarithmic property to simplify the equation: ln(5) + ln(e³ˣ) = ln(33).
3. Use the rule that ln(e) = 1 to simplify further: ln(5) + 3x = ln(33).
4. Subtract ln(5) from both sides of the equation: 3x = ln(33) - ln(5).
5. Divide both sides by 3 to solve for x: x = (ln(33) - ln(5)) / 3.

The value of x that makes the equation true is approximately x = 0.453.

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