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There exists a natural number N which i...

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

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To solve the problem, we need to find a natural number \( N \) such that: \[ N = 50 \cdot \log_{10}(N) \] ### Step 1: Rewrite the equation We can rewrite the equation as: ...
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CENGAGE ENGLISH-LOGARITHM-All Questions
  1. If (log)4 5=aa n d(log)5 6=b , then (log)3 2 is equal to 1/(2a+1) (b)...

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  2. If (log)(10)2=a ,(log)(10)3=bt h e n(log)(0. 72)(9. 6) in terms of a a...

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  3. There exists a natural number N which is 50 times its own logarithm t...

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  4. The value of ((log)2 24)/((log)(96)2)-((log)2 192)/((log)(12)2) is 3 (...

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  5. Find the number of solutions of equation (2x-3)2^x=1

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  6. Find the value of (log)(2sqrt(3))1728.

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  7. Prove that 1/3<(log)(10)3<1/2dot

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  8. Arrange (log)2 5,(log)(0. 5)5,(log)7 5,(log)3 5 in decreasing order.

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  9. If 3^x=4^(x-1) , then x= (2(log)3 2)/(2(log)3 2-1) (b) 2/(2-(log)2 3...

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  10. Solve: |x-3|^(3x^2-10 x+3)=1

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  11. Find the smallest integral value of x satisfying (x-2)^(x^2-6x+8))&gt...

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  12. The least value of the expression 2(log)(10)x-(log)x(0.01)dot for x &...

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  13. The solution of the equation (log)7(log)5(sqrt(x+5)+sqrt(x)=0 is...

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  14. Let (x0, y0) be the solution of the following equations: (2x)^(1n2)=(3...

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  15. If In(a+c),ln(a-c),ln(a-2b+c) are in AdotPdot, then a , b , c ,a r ...

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  16. Prove that number (log)2 7 is an irrational number.

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  17. Which of the following numbers are positive/negative? (log)2 7 (ii) (...

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  18. If (log)3 2,(log)3(2^x-5)a n d(log)3(2^x-7/2) are in arithmetic progre...

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  19. Solve x^((log)y x)=2a n dy^((log)x y)=16

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  20. Solve (log)(2x)2+(log)4 2x=-3//2.

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