algebra 2 problem

Question

In x + In (x+8) =1      ????

Answer 1

Hello Diane,

 

An excellent answer has been already given by Michael J., thus I am just adding couple words in regards to the computational part. Approximating the transcendental number e as 2.7182818, the following quadratic equation in its canonical form:

 

x² + 8x - 2.7182818 = 0

 

can be easily solved using online quadratic equation solver (http://examn8.com/QuadraticEquations.aspx), having two real solutions (rounded):

 

x1= 0.326462966442681
x2= -8.32646296644268

 

Pertinent to this particular problem (as commented by Mark M.), the second solution is not applicable, thus there is only one solution x1.

 

Hope this may help.

 

 

Answer 2

First, we use the addition property of logs.

 

ln(x(x + 8)) = 1

 

ln(x² + 8x) = 1

 

 

The solution to a natural log is the exponent of the base number e.

 

e¹ = x² + 8x

 

 

Subtract e on both sides of the equation.

 

0 = x² + 8x - e

 

 

Use the quadratic formula to solve for x.

 

x = (-b ± √(b² - 4ac)) / 2a

 

where:

a = 1

b = 8

c = -e

 

Plug in these values into the formula to solve for x.  Once you solved for x, validate the solutions by substituting them into the original equation.