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anonymous
 one year ago
help please
Solve 64^x = 16^x−1.
x = −2
x = −1
x = negative 1 over 4
x = negative 1 over 3
anonymous
 one year ago
help please Solve 64^x = 16^x−1. x = −2 x = −1 x = negative 1 over 4 x = negative 1 over 3

This Question is Closed

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0since \[4^2=16\] and \[4^3=64\] this is the same as \[\huge4^{3x}=4^{2(x1)}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1442080279656:dw

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0now that the bases are the same, solve by solving \[3x=2(x1)\] for \(x\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i sent a drawing of the problem

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0the idea is this: if \[\huge b^{\spadesuit}=b^{\heartsuit}\] then \[\spadesuit =\heartsuit\] in other words, if the bases are the same, then so are the exponents

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but the bases are not the same

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0that is why i made them the same did you look at the answer i wrote above? i arranged it so the bases were equal

Mr_Perfection_xD
 one year ago
Best ResponseYou've already chosen the best response.0looking for cheap & free medals

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0ok your two bases are 64 and 16 right?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0and they are not equal

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no they are not equal

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0but both 64 and 16 are powers of 4

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0because \[4^2=16\\ 4^3=64\] right?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0so...\[64^x=(4^3)^x=4^{3x}\] clear?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0how about \[16^{x1}\] can you do the same thing with that one, like i did with \(64^x\)?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0well actually \[\huge (4^2)^{x1}\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0which is the same as \[\huge 4^{2(x1)}\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0so now your equation looks like \[\huge 4^{3x}=4^{2(x1)}\]and the bases are now the same

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0that means the exponents must also be the same, i.e. \[3x=2(x1)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so would the answer be 1?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0can you solve \[3x=2(x1)\]?
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