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(a) Which is smaller ? 2 or (log(pi)...

(a) Which is smaller ? 2 or `(log_(pi) 2 + log_(2) pi)`.
(b) Prove that `log_(3) 5 " and " log_(2) 7 ` are both irrational.

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The correct Answer is:
(a) 2
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MOTION-BASIC MATHEMATIC & LOGARITHM -Exercise - 3
  1. 5^(log(1/5)(1/2)) +log(sqrt(2)) (4/(sqrt(7)+sqrt(3)))+log(1/2)(1/(10+2...

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  2. a) Calculate: 4^(5log(4sqrt(2))(3-sqrt(6))-6log(e)(sqrt(3)-sqrt(2))) ...

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  3. (a) Which is smaller ? 2 or (log(pi) 2 + log(2) pi). (b) Prove t...

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  4. Let A denotes the value of log10 {(ab+sqrt((ab)^2-4(a+b)))/2}+log10 {l...

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  5. Solve following log equation x^((logx+5)/3)=10^(5+logx)

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  6. If x, where 0,1,2 are respectively the values of x satisfying the equa...

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  7. log(4)(log(2)x)+log(2)(log(4)x)=2

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  8. Solve the equation 5^(x)root(x)(8^(x-1))=500

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  9. Given that log2(3)=a,log3(5)=b,log7(2)=c, express the logrithm of the ...

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  10. If log(b) a. log(c ) a + log(a) b. log(c ) b + log(a) c. log(b) c = 3 ...

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

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

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

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

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  15. 9^(1+log x)- 3^(1+log x) - 210 = 0 , where base of log is 3.

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

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

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

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

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

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