Solve For X Log2 3x1 Log2 x1 1 12 Solve For X 5x2 62x1Sol

Solve For X: Log_2 (3x-1) - Log_2 (x+1) = 1 12. Solve For X: 5^x-2 = 6^2x+1

1) log2(3x -1) - log2(x+1) =1

use the log property : logA - logB = log(A/B)

log2(3x-1)/(x+1) = 1

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

3x -1 = 2x +2

x = 3

12) 5^(x-2) = 6^(2x+1)

take natural log on both sides:

ln(5^(x-2)) = log(6^(2x+1))

(x-2)log5 = (2x +1)log6

x( log5 -2log6) = ( log6 +2log5)

x = ( log6 +2log5)/( log5 -2log6) = -2.538