Solve for X 33x 33x1 18SolutionWe have 33x 33x1 18 or 3 3

Solve for X.

3^(3x) - 3^(3x-1)= -18

Solution

We have 3^(3x) - 3^(3x-1) = -18 or, 3 *3^(3x-1) - 3^(3x-1) = -18 or, 2* 3^(3x-1) = -18 .

On dividing both the sides by 2, we get 3^(3x-1) = - 9 or, (3^3x) /3 = -9 or, 3^3x = -27 or, 27^x = -27 or, 27^(x-1) = -1. Now, on taking logarithm of both the sides, we get (x-1) log 27 = log (-1). Therefore, x-1 = log (-1)/log 27 = so that x = 1 + log (-1)/log 27 = 1 + (1.36437635 i / 1.431363764) = 1+ 0.953200286 i (approximately)