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.

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- October 28th 2008, 06:01 PMabey_27ALGEBRA 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. - October 28th 2008, 06:55 PMpythagSolution 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). - October 29th 2008, 08:55 AMthegarden
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 - October 29th 2008, 09:00 AMthegarden
- October 29th 2008, 09:31 AMthegarden
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