Question

Solve the following equations.
log(x) + log(x + 21) = 2

Answer 1

x = 4 , -25

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