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5^(x+1) - 3x5^(x-1) = 22....please help

Mathematics
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\[5^{(x+1)}(1-3) = 22 =>5^{(x+1)} = -11 =>x is imaginary\]
1 certainly works
\[5^2-3=25-3=22\]

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Other answers:

you can write \[5^{x+1}=5^2\times 5^{x-1}\] and the solve \[25\times 5^{x-1}-3\times f^{x-1}=22\] \[22\times 5^{x-1}=22\] \[5^{x-1}=1\] \[x-1=0\] \[x=1\]
that "f" in line 4 should be a "5"
btw 1 is not imaginary. just thought i would mention it
sorry .. i misread the second exponent as x+1
oh, guess there would be nothing then for sure!
Another version: \[5^{x+1} - 3\cdot5^{x-1} = 22\] \[5\cdot 5^x-\frac{3}{5}5^x=22\] \[25\cdot 5^x-3\cdot 5^x=110\] \[22\cdot 5^x=110\] \[5^x=5\] \[x=1\]

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