Question

How to find a.... a^7 =7777.
The problem is if a^7 = 7777 and (a^6)/(b) = 11 what is the value of ab.. The answer is apparently 707??

I don't understand how to get it. Please do it step by step please. Thank you! :D
I'm stuck. Can

Answer 1

\[\frac{ a ^{6} }{ b }=11->a ^{6}=11b\]
Multiply both sides by a
\[a ^{7}=11ab\] But a^7 = 7777, so:
\[7777=11ab\]

Answer 2

wow it was that easy. omg i'm really think way too hard for these problems...
- o -

Answer 3

And thank you again!
lol im going to fail the sat. >:

Answer 4

Lol, good luck. And np.

Answer 5

First, let's try to solve for 'a'
a^7 = 7,777
7*log(a) = log(7,777)
log(a) = 3.890812099/7
log(a) = 0.5558302999
10^0.5558302999 = a
a = 3.5960879092
and a^7 = 7,777

Answer 6

wow - I was typing all that (and didn't get the final answer) as Psymon was typing out a much more concise answer
Well I hope B2ST can use the value of 'a'

Answer 7

lol its okay.. I did similar to that.. - o -
sat questions is too tricky...

Answer 8

glad you came back B2ST
you pursued the less efficient route of taking logarithms of everything? LOL
By the way I gave Psymon a medal for his elegant answer.

Answer 9

Lol, to be honest, I wouldnt have even thought of brute-force solving for a. I figured there would just be a way to relate all of the given information. I solved for a^6 and then just saw what to do.

Answer 10

I think "brute force" and stick with it. (Not always a good thing to do).
But heck, we all know the value of 'a' now.

Answer 11

Lol, nvm xD

Answer 12

I'm taking these questions way too complicated. ; A;
I cant simplify my mind anymore. lol

Answer 13

if these are SAT practice questions they will purposely throw in problems that have a difficult solution AND an easy one. Example:
Which is larger?
a) 237/5,693 or b) 237/5,694
One solution takes the time the other solution is much quicker.

Answer 14

I'm using Baron's math work book. So the questions are more difficult than the SAT..

Answer 15

Well it's good to see you are not taking the easy route. LOL