How do you solve #8^ { x - 3} = 16^ { x}#?

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Answer 1 · 2017-06-05T02:33:21

#x=-9#

To solve this, we'd like to have the bases be the same. To get them equal, notice that they are both can be expressed in terms of base 2:

#8=2^3, 16=2^4=>(2^3)^(x-3)=(2^4)^x#

Now we can use the rule that where #(x^a)^b=x^(ab)#

#2^(3(x-3))=2^(4x)#

#2^(3x-9)=2^(4x)#

Which means:

#3x-9=4x#

#x=-9#