Solve. logx+log(x+21)=2

logx+log(x+21)=2

Rewrite the left side as

log [ x * (x + 21)]  = 2       and 2 can be written as log 100......so we have....

log [x ( x + 21) ]  = log 100      we can forget the logs and solve this:

x ( x + 21)   = 100    simplify

x^2 + 21x  = 100

x^2 + 21x - 100  = 0  factor as

(x + 25) ( x - 4)  = 0

Setting each factor to 0, x = -25  or x = 4

Reject -25 since it makes the logs negative

x= 4 is the soultion