Answer:
x² + 8x - 85 = 0
and, the roots are x = [tex]-4+\sqrt{101},\:x=-4-\sqrt{101}[/tex]
Step-by-step explanation:
Data provided:
log(x + 3) + log(x + 5) = 2 ..........(1)
Now,
From the properties of the log function, we know
log(A) + log(B) = log(AB)
therefore,
applying the above property in the equation (1), we get
log((x+3)(x+5)) = 2
or
log(x² + 3x + 5x + 15) = 2
taking the anti-log both sides, we get
x² + 3x + 5x + 15 = 10²
or
x² + 8x + 15 = 100
or
x² + 8x + 15 - 100 = 0
or
x² + 8x - 85 = 0
on solving the above equation
the roots are
x = [tex]-4+\sqrt{101},\:x=-4-\sqrt{101}[/tex]
