Solve (log_{2}(12x – 10) = 1 + log_{2}(4x + 3)).
-
A.
4.75 -
B.
4.00 -
C.
1.75 -
D.
1.00
Correct Answer: Option B
Explanation
(log_{2}(12x – 10) = 1 + log_{2}(4x + 3))
Recall, ( 1 = log_{2}2), so
(log_{2}(12x – 10) = log_{2}2 + log_{2}(4x + 3))
= (log_{2}(12x – 10) = log_{2}(2(4x + 3)))
(implies (12x – 10) = 2(4x + 3) therefore 12x – 10 = 8x + 6)
(12x – 8x = 4x = 6 + 10 = 16 implies x = 4)