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

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

Solve
4^x + 128 = 9.2^x+2

2. ## ????

is it (9.2)^x or 9(2)^x

3. its (9.2)^x+2

4. 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)

5. 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

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

7. deej813, is this the equation that you want to be solved?

i don't know how to deal with this without resorting to graphing.
the blue line is the graph of the left hand side ()
the red line is the graph of the right hand side ()

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

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But what if what HE meant was ?

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Integer solutions are x1 = 2 and x2 = 5.
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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?

### solve for x when x is a power

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