Question

If log x + log (x + 3) = 1 then the value(s) of x will be, the solution of the equation

Answer 1

Hey there !

log a + log b = log ( a × b ) => Property of Log function.

So applying this property we get,

log x + log ( x + 3 ) = 1

=> log ( x ( x + 3 ) ) = 1

=> log ( x² + 3x ) = 1

=> x² + 3x = n¹ ( n = Base )

According to the question base is 10.

So x² + 3x = 10

=> x² + 3x - 10 = 0

=> x² + 5x - 2x - 10 = 0

=> x ( x + 5 ) - 2 ( x + 5 )

=> ( x - 2 ) ( x + 5 ) = 0

=> x = 2, -5

So the solutions of x are -5 and 2.

Hope my answer helped !