Question

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

Answer 1

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

Answer 2

1 certainly works

Answer 3

\[5^2-3=25-3=22\]

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

oh, guess there would be nothing then for sure!

Answer 9

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