How to find x, #x^5=9#?

Question

Eli Assouline · Accepted Answer

#x = root5(9) = 1.5518...#

Apply the same principles as with other equations....

You want to isolate #x# on the left.

Whatever you do on the left you must do on the right,

To get rid of the #5th# power, find the #5th# root.

#x^5 =9#

#root5(x^5) = root5(9)#

#x= root5(9)#

This is an irrational number, but using a calculator will give you:

#x = 1.5518..#

If you estimate an answer this seems right.

#1^5 = 1" "and" "2^5 = 32#

Therefore #9# has to be #1# raised to #1.??????#

#1^1.5518 =9#

Genesis Allen · Answer

Another approach option

#x~~1.5518# to 4 decimal places

Uses what they now call log inverse. Way, way back when I was at school they called them 'antilogs'. It reverses the process of taking a log so that you end up at the source number. Given: #x^5=9# Taking logs of both sides. I chose log to base 10 #log_10(x^5)=log_10(9)# #5log_10(x)=log_10(9)# #log_10(x)=log_10(9)/5# #x=log_10color(white)()^(-1)(( log_10(9))/5)# #x=1.5518455......# #x~~1.5518# to 4 decimal places