# ALGEBRA URGENT!! thank you

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• Oct 28th 2008, 05:01 PM
abey_27
ALGEBRA URGENT!! thank you
7 × 10^6 divided by a × 10^n is equal to 8.75 × 10^9
a is greater or equal to 1 but less than 10.
Find the value of a and the value of n.
• Oct 28th 2008, 05:55 PM
pythag
Solution involves logs and inequalities.
(7X10^6)/(aX10^n) = 8.75X10^9 where a>=1 and a<10.

7X10^6 = aX10^n X 8.75X10^9

1/8.75 = aX10^(n+9-6)

0.8 = aX10^(n+3)

8/10 = aX10^(n+3)

8 = aX10^(n+3) X 10^1

8 = aX10^(n+3+1)

8 = aX10^(n+4)

a = 8/[10^(n+4)]

a>=1

8/[10^(n+4)]>=1

8>=10^(n+4)

log8>=log10^(n+4)

log8>=(n+4)log10

log8>=(n+4)(1) (since log10 =1)
log8>=n+4
log8-4>=n
-3.096910013>=n

or

a<10

8/[10^(n+4)]<10

8<10X10^(n+4)

8<10^(n+4+1)

8<10^(n+5)
log8<log10^(n+5)
log8<(n+5)log10
log8<(n+5)(1) (since log10 = 1)

log8<n+5
log8-5<n
0.4771212547<n

(I am not sure if the above solution is correct. It seems too involved. I feel that there might be an easier solution. I sure would like to know what it is. Cheers Abey(Cool)(Yes).
• Oct 29th 2008, 07:55 AM
thegarden
Sorry this is late abey, but hope it helps...

7 x 10^6 = 8.75 x 10^9
a x 10^n

multiply through by a x 10^n, so you get:

7 x 10^6 = a x 10^n
8.75 x 10^9

therefore a = 7/8.75=0.8

and n = 6-9 = -3
• Oct 29th 2008, 08:00 AM
thegarden
Quote:

Originally Posted by thegarden
Sorry this is late abey, but hope it helps...

7 x 10^6 = 8.75 x 10^9
a x 10^n

multiply through by a x 10^n, so you get:

7 x 10^6 = a x 10^n
8.75 x 10^9

therefore a = 7/8.75=0.8

and n = 6-9 = -3

EDIT: I have just re-read the question. It states: a is greater or equal to 1 but less than 10. So i am not sure if my solution is correct.
• Oct 29th 2008, 08:31 AM
thegarden
I think i have the correct solution now:

working through it again...

7 x 10^6 = 8.75 x 10^9
a x 10^n

multiply through by a x 10^n, so you get:

7 x 10^6 = a x 10^n
8.75 x 10^9

Simplifying, 0.0008 = a x 10^n

0.0008 is the same as 8 x 10^-4

So a=8 and n = -4