Log (x+21)+logx=2 solve the equation

The sum of logs is the log of the product.

Law of logarithms:

Apply the law above to the left side of the equation.

Now use the definition of log.

x = -21 must be discarded because log (x + 21) would become log (-21) which is not defined.

Solution: x = 4

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is