Question

Solve : log2 (x + 5) – log2 (2x - 1) = 5​

Answer 1

Explanation:

log2 (x + 5) - log2 (2x - 1) = 5

log2 [(x + 5)/(2x - 1)] = 5

2^5 = (x + 5)/(2x - 1)

32 = (x + 5) /( 2x - 1)

32(2x - 1) = x + 5

64x - 32 = x + 5

63x = 37

x = 37/63

Answer 2

Answer:

$log_{2}(x + 5) - log_{2}(2x - 1) = 5 \\ log_{2}( \frac{x + 5}{2x - 1} ) = 5 \\ \frac{x + 5}{2x - 1} = {2}^{5} \\ \frac{x + 5}{2x - 1} = 32 \\ x + 5 = 32(2x - 1) \\ x + 5 = 64x - 32 \\ 64x - x = 32 + 5 \\ 63x = 37 \\ \boxed{ x = \frac{37}{63} }$

• x=37/63 is the right answer.