Question

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

Answer 1

Is that 2^(x+1)?

Answer 2

yes

Answer 3

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

Answer 4

so x=3/2?

Answer 5

No. How did you come to that answer?

Answer 6

reducing? im really not good at math

Answer 7

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.

Answer 8

x would = 2

Answer 9

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)

Answer 10

x=7/2?

Answer 11

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

Answer 12

yes you smart cookie. thankyou!!

Answer 13

:) Np