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Mathematics 18 Online
OpenStudy (anonymous):

solve for x: 2^x+1=8^x-2

OpenStudy (anonymous):

Is that 2^(x+1)?

OpenStudy (anonymous):

yes

OpenStudy (anonymous):

Note you can write 8 as 2^3. Try using that

OpenStudy (anonymous):

so x=3/2?

OpenStudy (anonymous):

No. How did you come to that answer?

OpenStudy (anonymous):

reducing? im really not good at math

OpenStudy (anonymous):

So we can substitute 2^3 for 8 right. It becomes 2^(x+1)=[2^3]^(x-2). The right hand side can be simplified 2^(x+1)=2^3(x-2) Since the bases are the same, the exponents must be equal.

OpenStudy (anonymous):

x would = 2

OpenStudy (anonymous):

Did you equate the exponents: Like if i say a^x=a^y, x must be equal to y. So in our case x+1=3(x-2)

OpenStudy (anonymous):

x=7/2?

OpenStudy (anonymous):

Yes. Do you see how the substitution helped? It made the bases the same so we can conclude that the exponents are equal

OpenStudy (anonymous):

yes you smart cookie. thankyou!!

OpenStudy (anonymous):

:) Np

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