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Find the sum and product of all possibl...

Find the sum and product of all possible values of x which makes the following statement true.
`log_(6)54+log_x16=log_sqrt2x-log_36(4/9)` .

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The correct Answer is:
Sum=`9/2`, product=2
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ARIHANT MATHS-LOGARITHM AND THEIR PROPERTIES-Exercise (Subjective Type Questions)
  1. Solve the following inequation . (xv) x^((log10x)^2-3log10x+1)gt1000

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

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  3. Solve the following inequation . (xvii) log2(9-2^x)le10^(log10(3-x))

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

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  5. Every Natural number is Whole number?

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  6. Find the value of x of log(4)x = 2

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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. Every Integer is Whole number?

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  16. Every Whole number Integer ?

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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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