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How do you solve #2^x=4^(x+1)#?

1 Answer

Aug 22, 2015

Re-express the right hand side as #2^(2x+2)# to find #x = -2#

Explanation:

#(a^b)^c = a^(bc)# and #4 = 2^2#, so...

#2^x = 4^(x+1) = (2^2)^(x+1) = 2^(2(x+1)) = 2^(2x+2)#

So #x = 2x+2#

Subtract #(x + 2)# from both sides to get #x = -2#

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