Question

Please help:


`5^(x-1) + 5` x
`0.2^(x-2) = 26`



When I tried it, I got up until canceling the 5s and getting x - 1 - x - 2 = 21

What did I do wrong?

Answer 1

`5^(x-1)+5*0.2^(x-2)=26\\ 5^(x-1)+ (1)/(5^(x-3)) =26\\ 25*5^(x-3)+(1)/(5^(x-3)) =26\\ Assume\ y=5^(x-3)\\ 25y+ (1)/(y)=26\\ 25y^2-26y+1=0\\ \Delta=(-26)^2-4*25=576=24^2\\ y= (26+24)/(50) =1 \ or\ y= (26-24)/(50) = (1)/(25) \\ if\ y=1\ then 5^(x-3)=1==\ \textgreater \ x-3=0==\ \textgreater \ x=3\\ if\ y= (1)/(25)\ then\ 5^(x-3)=(1)/(5^2)==\ \textgreater \ x-1=0==\ \textgreater \ x=1\\`