1. anonymous

$5^{(x+1)}(1-3) = 22 =>5^{(x+1)} = -11 =>x is imaginary$

2. anonymous

1 certainly works

3. anonymous

$5^2-3=25-3=22$

4. anonymous

you can write $5^{x+1}=5^2\times 5^{x-1}$ and the solve $25\times 5^{x-1}-3\times f^{x-1}=22$ $22\times 5^{x-1}=22$ $5^{x-1}=1$ $x-1=0$ $x=1$

5. anonymous

that "f" in line 4 should be a "5"

6. anonymous

btw 1 is not imaginary. just thought i would mention it

7. anonymous

sorry .. i misread the second exponent as x+1

8. anonymous

oh, guess there would be nothing then for sure!

9. anonymous

Another version: $5^{x+1} - 3\cdot5^{x-1} = 22$ $5\cdot 5^x-\frac{3}{5}5^x=22$ $25\cdot 5^x-3\cdot 5^x=110$ $22\cdot 5^x=110$ $5^x=5$ $x=1$