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There exists a natural number N which is...

There exists a natural number `N` which is 50 times its own logarithm to the base 10, then `N` is divisible by

A

5

B

7

C

9

D

11

Text Solution

Verified by Experts

The correct Answer is:
A
`N= 50 log_(10) N`
` rArr log_(10) N = N/50`
` rArr N = (10) ^(N//50)`
` rArr N^(1//N) = (10)^(1//50) = (10)^(2//100)= (100)^(1//100`
` :. N = 100`
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CENGAGE-LOGARITHM AND ITS PROPERTIES-Exercise (Single)
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  3. There exists a natural number N which is 50 times its own logarithm to...

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  4. The value of ((log)2 24)/((log)(96)2)-((log)2 192)/((log)(12)2) is

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  5. log(x-1)x*log(x-2)(x-1)*...*log(x-12)(x-11) = 2,x is equal to

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  6. If f.(x)= log((1+x)/(1-x)), then

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  7. If a^4b^5=1 then the value of loga(a^5b^4) equals

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  8. The value of 3^((log)4 5)-5^((log)4 3) is 0 (b) 1 (c) 2 (d) none of...

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  9. If 2^(x+y) = 6^(y) and 3^(x-1) = 2^(y+1), then the value of (log 3 - l...

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  10. The value of x satisfying sqrt3^(-4+2log(sqrt5)x)= 1//9 is

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  11. The value of x satisfying the equation root(3)(5)^(log(5)5^(log(5)5^...

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  12. If sqrt((log)2x)-0. 5=(log)2sqrt(x ,) then x equals

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  13. If log(y) x + log(x) y = 2, x^(2)+y = 12 , then the value of xy is

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  14. 4^(log9 3)+9^(log2 4)=1 0^(logx 83), then x is equal to

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  15. Solve (x+1)^(log(10) (x+1))=100(x+1)

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  16. If log2x+logx2=10/3=log2y+logy2 and x!=y ,then x+y=

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  17. If (log)(10)[1/(2^x+x-1)]=x[(log)(10)5-1] , then x= 4 (b) 3 (c) 2 ...

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  18. If (log)3{5+4(log)3(x-1)}=2, then x is equal to 4 (b) 3 (c) 8 (d) (...

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  19. If 2x^(log(4)3)+3^(log(4)x)= 27, then x is equal to

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  20. The equation log4(2-x)+log(0.25)(2+x)=log4(1-x)+log(0.25)(2x+1) has

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