Answer:
x = 4 , -25
Step-by-step explanation:
given,
log(x) + log(x + 21) = 2
using identity
log (ab) = log a + log b
log(x) + log(x + 21) = log (x (x + 21))
log (x (x + 21)) = 2
now taking anti log as base is ( 10)
x(x+ 21 ) = 10²
x² + 21 x - 100 = 0
x² + 25 x - 4 x - 100 = 0
x(x + 25) -4 (x + 25) = 0
(x-4)(x + 25) = 0
x = 4 , -25
hence, the solution is x = 4 , -25
