Question

solve: 2^x=8^x+2

Answer 1

2^x = (2^3)^x + 2

Answer 2

2^x = 2^(3x) + 2

Answer 3

factor out 2

Answer 4

2 (2^(x-1) ) = 2 (2^(3x-1) ) + 2

Answer 5

cancel off 2s

Answer 6

2^(x-1) = 2^(3x-1) +1

Answer 7

I would probably move both over to the LHS

Answer 8

2^(x-1) -2^(3x-1) = 1

Answer 9

take ln of both sides

Answer 10

ln [ 2^(x-1) -2^(3x-1) ] = ln(1)

Answer 11

dont think that did anything :|

Answer 12

This has no solutions

Answer 13

small proof would be let a = 2^x, so then a^3 = 8^x, so we get a^2 = a^3 + 2 so a^3 - a^2 + 2 = 0, from judge if a = -1, then -1 -1 + 2 = 0, so a = -1, then 2^x = -1, which is impossible, since 2^x is always more then 0. hope this helps, favourite me if it did :)

Answer 14

You there, does that make sense?

Answer 15

Yea, i think i get it, working it out again to make sure!! thank you both.