In Exercises 79–84, solve for y.
79. 3^y = 2^(y+1)

Evaluate the integrals in Exercises 31–78.

47. ∫(1/r)csc²(1+ln(r))dr

133. What is the age of a sample of charcoal in which 90% of the carbon-14 originally present has decayed?

In Exercises 1–24, find the derivative of y with respect to the appropriate variable.

3. y = (1/4)xe^(4x) - (1/16)e^(4x)

Evaluate the integrals in Exercises 31–78.

41. ∫(from 0 to 4)2t/(t² - 25)dt

In Exercises 1–24, find the derivative of y with respect to the appropriate variable.

17. y = ln(arccos(x))

Evaluate the integrals in Exercises 31–78.

37. ∫(from -1 to 1)dx/(3x-4)