Question

solve the logarithm
log_2 (x -1)- log_2(5x +1) = -3

I got -3, is this correct???????

Answer 1

assuming base 2 for ease of reading,

log(x-1) - log(5x+1) = -3
log[(x-1)/(5x+1)] = -3
(x-1)/(5x+1) = 2^-3 = 1/8
8(x-1) = 5x+1
8x - 8 = 5x + 1
3x = 9
x = 3

log 2 - log 16 = 1 - 4 = -3