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If P is the number of natural number wh...

If P is the number of natural number whose logarithms to the base 10 have the characteristic p and Q is the number of natural numbers logarithms of whose reciprocals to the base 10 have the characteristic -q, then find the value of ` log_(10)P-log_(10) Q`.

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The correct Answer is:
`=p-q+1`
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ARIHANT MATHS ENGLISH-LOGARITHM AND THEIR PROPERTIES-Exercise (Subjective Type Questions)
  1. Solve the following inequation . (xiv) log((3x^2+1))2lt1/2

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  2. Solve the following inequation . (xv) x^((log10x)^2-3log10x+1)gt1000

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  3. Solve the following inequation . (xvi) log4{14+log6(x^2-64)}le2

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  4. Solve the following inequation: 2x+3<5x-4

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  5. Solve the following inequation . (xix) 1+log2(x-1)lelog(x-1)4

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  6. Solve the following inequation . (xx) log(5x+4)x^2lelog(5x+4)(2x+3)

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  7. 2^((sqrt(loga(ab)^(1//4)+logb(ab)^(1//4))-sqrt(loga(b/a)^(1//4)+logb(a...

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  8. It is known that x=9 is root of the equation.loglamda(x^2+15a^2)-logla...

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  9. Solve log4(log3x)-log(1//4)(log(1//3)y)=0 and x^2+y^2=17/4.

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  10. Find dy/dx if log(4x)+log(16x)=4y.

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  11. Find the sum and product of all possible values of x which makes the ...

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  12. Solve : (3)/(2)log(4)(x+2)^(2)+3=log(4)(4-x)^(3)+log(4)(6+x)^(3).

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  13. Find the number of real values of x satisfying the equation. log(2)(...

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  14. Solve the system of equation 2^(sqrtx+sqrty)=256 and log10sqrt(xy)-log...

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  15. Solve the system of equations log2y=log4(xy-2),log9x^2+log3(x-y)=1.

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  16. The values of x satisfying 2log((1)/(4))(x+5)gt(9)/(4)log((1)/(3sqrt(3...

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  17. Solve log3(sqrtx+|sqrtx-1|)=log9(4sqrtx-3+4|sqrtx-1|).

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  18. In the equality (log2x)^4-(log(1//2)"x^5/4)^2-20log2x+148lt0 holds...

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  19. Find the value of x satisfying the equation, sqrt((log3(3x)^(1/3)+logx...

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  20. If P is the number of natural number whose logarithms to the base 10 ...

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