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If 6^(x-y)=36 and 3^(x+y)=729, then find...

If `6^(x-y)=36` and `3^(x+y)=729`, then find `x^(2)-y^(2)`.

A

12

B

4

C

24

D

8

Text Solution

Verified by Experts

The correct Answer is:
A
`6^(x-y)=36`
`6^(x-y)=6^(2)`
`:. x-y=2` (1)
and `3^(x+y)=3^(6) implies x+y=6` (2)
From (1) and (2), `x^(2)-y^(2)=12`.
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PEARSON IIT JEE FOUNDATION-INDICES-CONCEPT APPLICATION LEVEL 2
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  5. If a^x = b^y = a^z and a^3 = b^2 c, then 3/x - 2/y =

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  6. Simplified form of ((p+1/q)^((p-q))(p-1/q)^((p+q)))/((q+1/p)^((p-q))(...

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  7. If X = a^1 b^2 c^3 ... z^26 and Y = z^1 y^2 x^3... a^26 where, abcd...

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  8. If a^(b)=256, then find the maximum possible value of a.b, where a and...

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  13. If 5^(n-3)=625, then 5^(n+3) is .

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  14. Find the value of (0.00243)^(3/5)+(0.0256)^(3/4).

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  15. [((a^(0)+b^(0))(a^(0)-b^(0)))/(a^(2)-b^(2))]^(0^(+^(5)))" "("where "...

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  16. If (1331)^(-x)=(225)^(y) where x and y are integers, then find the val...

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  17. If (sqrt(3))^(x+y)=9 and (sqrt(2))^(x-y)=32, then 2x+y is .

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  18. If 6^(x-y)=36 and 3^(x+y)=729, then find x^(2)-y^(2).

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  19. If p^(q')=512 find the minimum possible value of (p) (q) (r), where p,...

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  20. If 2^(x+y)=128 and 4^(x-y)=16, then find x/y.

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