Question

logof3(x-1)+ logof3(3x-1)=2

Answer 1

Log((3X - 3)(9X - 3)) = 2.

(3X - 3)(9X - 3) = 10^2,
27X^2 - 9X - 27X + 9 = 100,
27X^2 - 36X + 9 = 100,
27X^2 - 36X + 9 - 100 = 0,
27X^2 - 36X - 91 = 0,

Using the Quadratic Formula:
X = (36 +- sqrt(1296 - (- 9828))) / 54,
X = (36 +- sqrt(1296 + 9828)) / 54,
X = (36 +- sqrt(11124)) / 54,
X = (36 +- 105.5) / 54,

X = 2.62, and X = -1.29.

Check:
Log((3*2.62 - 3)(9*2.62 - 3) =
Log(7.86 - 3)(23.58 - 3) =
Log(4.86 * 20.58) =

Log(100.019) = 2.000.