Question

Find all the real-number roots of the equation. Give an exact expression for the root and also a calculator approximation rounded to three decimal places. (Enter your answers as comma-separated lists.)
log9(x^2 + x) = 0.5

Answer 1

log9(x^2 + x) = 0.5
x^2 +x = 9^(1/2) = 3
x^2 +x - 3 = 0
Delta = 1 + 12 = 13
x = -1 +/- sqrt (13)/ 2

Answer 2

You can plug the numbers into your calculator now!