Solve the following logarithmic equation log2x 7 4 log2x

Solve the following logarithmic equation. log_2(x + 7) = 4 - log_2(x + 1) Select the correct choice below and, if necessary, fill in the answer box to complete your choi The solution set is There is no solution.

Solution

log2(x +7) = 4 -log2(x+1)

log2(x +7) + log2(x+1) = 4

use the log property : loga +logb = log(a*b)

log2(x+7)(x+1) =4

(x+7)(x+1) = 2^4

x^2 + 8x +7 = 16

x^2 +8x -9 =0

x^2 +9x -x -9 =0

x(x +9) -1(x+9) =0

(x-1)(x +9) =0

x = 1 ; x =-9

Now x +1 >0 --> x >-1

So, solution set : x = 1