Hopefully this should be a quick questions.
When solving the exponential equation 5 * 2^(u/2) + 30 = 600
Why do you subtract 30 first and not divide 600 by 5? The order of operations indicates that you would divide first and then subtract afterwards.
The answer in the book indicates that you do the following:
5 * 2^(u/2) = 570
2^(u/2) = 114
ln(2^(u/2) = ln114
(1/2)uln2 = ln114
uln2 = 2ln114
u = (2ln114)/ln2
u=13.665
Thanks.
You can divide through by $5$ first. You'd get $$5\cdot 2^{u/2} + 30 = 600 \iff 2^{u/2}+6 = 120\iff 2u^{1/2} = 120 - 6 = 114$$
Then you can subtract six from both sides. Just remember when dividing an equation by a non-zero term, you need to divide each term in a sum or difference. E.g. Suppose we have the equation $2a + 6 =10$. Then $$2a + 6 = 10\iff \frac 12(2a + 6) = \frac 12\cdot 10 \iff \frac 12(2a) + \frac 12(6) = 5\iff a + 3 = 5$$