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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)
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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 . (xviii) loga((2x+3)/x)ge0 for (a) a...

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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. Solve sqrt(logx(a x)^(1/5)+loga(a x)^(1/5))+sqrt(loga(x/a)^(1/5)+logx(...

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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 the real values (s) of x satisfying the equation log(2x)(4x)+log(...

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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. Solve log2(4^(x+1)+4).log2(4^x+1)=log(1//sqrt2)(1/sqrt8).

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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. Find the solution of the inequality 2log(1/4)(x+5)>9/4log(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 numbers whose logarithms to the base 10 ...

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