Asked by Anonymous
Assume that x, y, and z are positive numbers. Use the properties of logarithms to write the expression 2lnx - 6lny + 1/3ln e^12 as a simplified logarithm.
Is this 2lnx - 6lny + 4, or can it be simplified further?
Is this 2lnx - 6lny + 4, or can it be simplified further?
Answers
Answered by
Steve
you are correct as far as you went, but recall that n*ln(x) = ln(x^n).
2lnx - 6lny + 1/3ln e^12
= ln(x^2) - ln(y^6) + (1/3)(12)
= ln(x^2/y^6) + 4
= ln(e^4 x^2/y^6)
2lnx - 6lny + 1/3ln e^12
= ln(x^2) - ln(y^6) + (1/3)(12)
= ln(x^2/y^6) + 4
= ln(e^4 x^2/y^6)