Homework Help

Solve the equation 4^(x^2 - 8) = 10^(2x)

user profile pic

lxsptter | Student, Undergraduate | Valedictorian

Posted July 3, 2013 at 2:40 PM via web

dislike 1 like

Solve the equation 4^(x^2 - 8) = 10^(2x)

1 Answer | Add Yours

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 3, 2013 at 2:48 PM (Answer #1)

dislike 1 like

The equation `4^(x^2 - 8) = 10^(2x)` has to be solved.

Here it is not possible to equate the base for the left hand side and the right hand side. Take the logarithm of both the sides:

`log(4^(x^2 - 8)) = log(10^(2x))`

=> `(x^2 - 8)*log 4 = 2x*log 10`

=> `(x^2 - 8)*log 4 = 2x*1`

=> `log 4*x^2 - 2x - 8*log 4 = 0`

The roots of this quadratic equation are:

`(2 +- sqrt(4 + 4*log 4*8*log 4))/(2*log 4)`

= `(1 +- sqrt(1 + 1*log 4*8*log 4))/(log 4)`

= `1/(log 4) +- sqrt(1 + 8*(log 4)^2)/(log 4)`

`~~ 4.94` and `-1.61`

The solution of the given equation is approximately 4.94 and -1.61

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes