Question

Solve for y. Approximate by rounding your answer to places. 3e²ʸ+³=15 Show your work here

Answer 1

To solve for y in the equation 3e²ʸ+³=15, you need to isolate y. By subtracting 3 from both sides of the equation, dividing by 3, and applying logarithmic properties, the value of y can be approximated as log₂(1.386) in order to round the answer to the desired number of decimal places.

Step-by-step explanation:

1. Subtract 3 from both sides of the equation: 3e²ʸ = 12
2. Divide both sides of the equation by 3: e²ʸ = 4
3. Take the natural logarithm (ln) of both sides of the equation: ln(e²ʸ) = ln(4)
4. Use the logarithm property to bring down the exponent: 2ʸ * ln(e) = ln(4)
5. Since ln(e) = 1, the equation simplifies to 2ʸ = ln(4)
6. Take the logarithm base 2 of both sides of the equation: log₂(2ʸ) = log₂(ln(4))
7. Use the logarithm property to bring down the exponent: y * log₂(2) = log₂(ln(4))
8. Since log₂(2) =1, the equation simplifies to y = log₂(ln(4))
9. Approximately, y ≈ log₂(1.386)