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If x = log(3) 4 " and " y = log(5) 3, fi...

If `x = log_(3) 4 " and " y = log_(5) 3`, find the value of `log_(3) 10 " and " log_(3) (1 . 2)` in terms of x and y .

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The correct Answer is:
`(xy + 2)/ (2y) , (xy + 2y - 2)/(2y)`
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MOTION-BASIC MATHEMATIC & LOGARITHM -Exercise - 3
  1. If log(b) a. log(c ) a + log(a) b. log(c ) b + log(a) c. log(b) c = 3 ...

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  2. If (loga)/(b-c) = (logb)/(c-a) = (logc)/(a-b), then prove that a^(a)...

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  3. If x = log(3) 4 " and " y = log(5) 3, find the value of log(3) 10 " an...

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  4. If k^(log2 5)=16 , find the value of k^((log2 5)^2)

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  5. If log(10) (x^(2) - 12x + 36) = 2 , find x

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  6. 9^(1+log x)- 3^(1+log x) - 210 = 0 , where base of log is 3.

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  7. Solve for x: log(4) log(3) log(2) x = 0.

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  8. If log(e) log(5) [sqrt(2x - 2) +3 ] = 0

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  9. Let a and b be real numbers greater than 1 for which there exists a po...

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  10. Find the square of the sum of the roots of the equation log(3)x.log(...

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  11. Find 'x' satisfying the equation 4^(log(10) x + 1) - 6^(log(10)x) - ...

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  12. Given log(2) a = s, log(4) b = s^(2)" and " log(c^(2)) (8) = 2/(s^(3) ...

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  13. prove that a^x - b^y = 0 where x = sqrt(loga b ) and y = sqrt(logb ...

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  14. If x ,\ y >=0,(log)y x+(log)x y=(10)/3\ a n d\ x y=144 ,\ t h e n(x...

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  15. log(x+1)(x^2+x-6)^2=4

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  16. Solve the equation for x : log4+(1+1/(2x))log3=log(3x+27)

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  17. The real x and y satisfy log(8) x + log(4) y^(2) = 5 " and " log(8) y ...

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  18. If x=1+loga bc, y=1+logb ca, z=1+logc ab then prove that xyz=xy+yz+z...

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  19. Find the product of the positive roots of the equation sqrt((2008))...

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  20. Solve the following linear equations (i) |x| + 2 = 3 (ii) |x| - 2x...

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