How do you solve #x^ { 7} = 81x ^ { 5}#?

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Answer 1 · 2017-03-11T23:09:22

See the entire solution process below:

First, subtract #color(red)(81x^5)# from each side of the equation to set the equation equal to #0#:

#x^7 - color(red)(81x^5) = 81x^5 - color(red)(81x^5)#

#x^7 - 81x^5 = 0#

Next, factor #x^5# from each term:

#x^5(x^2 - 81) = 0#

Next solve each term for #0#:

Solution 1)

#x^5 = 0#

#x = 0#

Solution 2)

#x^2 - 81 = 0#

#x^2 - 81 + color(red)(81) = 0 + color(red)(81)#

#x^2 - 0 = 81#

#x^2 = 81#

#sqrt(x^2) = +-sqrt(81)#

#x = +-9#

The solution is #x = 0# and #x = 9# and #x = -9#