I have the equation:
16^n < 8^(n+1)
And need to solve for n.
What I did:
8^(4/3) = 16
n < (4/3)(n+1)
n < 4/3n + 4/3
3n < 4n + 4
-n < 4
n > 4
But, in the back of the book the answer is n < 3. What did I do wrong?
I have the equation:
16^n < 8^(n+1)
And need to solve for n.
What I did:
8^(4/3) = 16
n < (4/3)(n+1)
n < 4/3n + 4/3
3n < 4n + 4
-n < 4
n > 4
But, in the back of the book the answer is n < 3. What did I do wrong?
Your claim is correct: $\displaystyle 8^{4/3} =16$. So that implies that the inequality can be written as:
$\displaystyle (8^{4/3})^n < 8^{n+1}\implies 8^{4n/3}<8^{n+1}$
So this is true when $\displaystyle \frac{4}{3}n<n+1$ and this will give you the conclusion that's desired ($\displaystyle n<3$).
I hope this clarifies things.