# how do you solve for x when x is a power?

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• Aug 26th 2009, 10:27 PM
deej813
how do you solve for x when x is a power?
Solve
4^x + 128 = 9.2^x+2
• Aug 26th 2009, 10:42 PM
nikhil
????
is it (9.2)^x or 9(2)^x
• Aug 26th 2009, 10:45 PM
deej813
its (9.2)^x+2
• Aug 26th 2009, 11:06 PM
khotso
here is my try
4^x + 128 = 9.2^x+2
arrenge the eguatio to get
4^x-9.2^x=-126
9.2^x+4^x=126
take logarithm
log(9.2^x)+log(4^x)=log126
xlog9.2+xlog4=196
x(log9.2+log4)=196
x=196/(log9.2+log4)
• Aug 26th 2009, 11:08 PM
deej813
sorry its (9.2)^(x+2) x+2 is the power
could you possibly do it without logs please because i havn't learnt them yet
• Aug 27th 2009, 04:08 AM
aidan
Quote:

Originally Posted by deej813
sorry its (9.2)^(x+2) x+2 is the power
could you possibly do it without logs

YES.
• Aug 27th 2009, 05:46 AM
pacman
deej813, is this the equation that you want to be solved?

http://www4a.wolframalpha.com/Calcul...image/gif&s=38

i don't know how to deal with this without resorting to graphing.
http://www4a.wolframalpha.com/Calcul...image/gif&s=38 the blue line is the graph of the left hand side (http://www4a.wolframalpha.com/Calcul...image/gif&s=56)
the red line is the graph of the right hand side (http://www4a.wolframalpha.com/Calcul...image/gif&s=12)

the intersection of the two lines is the solution, x = 0.191

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But what if what HE meant was http://www4a.wolframalpha.com/Calcul...image/gif&s=23 ?

--------------------------------------------------------------------------------
Integer solutions are x1 = 2 and x2 = 5.
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(Shake)(Clapping)(Clapping)(Shake) (Wait)

http://www4a.wolframalpha.com/Calcul...image/gif&s=23
++++++++++++++++++++++++++++++++++++++++++

Again, the blue thread is the left hand side of the equation,
the red thread is the right hand side of the equation, the intersection of the two is the solution. Will they ever meet?