Homework Help

What is the solution of the exponential equation 9^(6 - x) - 8^x=0?

user profile pic

greynose | Student, Undergraduate | Honors

Posted May 14, 2011 at 3:11 PM via web

dislike 0 like

What is the solution of the exponential equation 9^(6 - x) - 8^x=0?

2 Answers | Add Yours

user profile pic

giorgiana1976 | College Teacher | Valedictorian

Posted May 14, 2011 at 3:33 PM (Answer #1)

dislike 0 like

We'll shift 8^x to the right side and we'll use logarithms to solve exponential equation.

We'll take the natural logarthim both sides:

ln 9^(6 - x) = ln 8^x

We'll apply the power rule for logarithms:

(6 - x)*ln 9 = x*ln 8

We'll re-write the equation:

6*ln 9 - x*ln 9 = x*ln 8

We'll add x*ln 9 both sides:

x*ln 9 + x*ln 8 = 6*ln 9

We'll factorize by x:

x*(ln 9 + ln 8) = ln 9^6

We'll divide by (ln 9 + ln 8):

x = ln 9^6/ln (8*9)

x = 13.1833/4.2766

The solution of the equation, rounded to four decimal places, is: x = 3.0826.

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 14, 2011 at 4:02 PM (Answer #2)

dislike 0 like

The equation to be solved is 9^(6 - x) - 8^x = 0.

9^(6 - x) - 8^x = 0

=> 9^(6 - x) = 8^x

=> 9^6/9^x = 8^x

=> 9^6 = (9^x)(8^x)

=> 9^6 = 72^x

It is not possible to equate the base of both the sides, so we can use logarithm

6*log 9 = x*log 72

=> x = 6*log 9/log 72

=> x = 3.0826 ( approximately)

The solution of the equation is x = 3.0826

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes