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Find the least value of log2x-logx(0.125...

Find the least value of` log_2x-log_x(0.125)`for `xgt1` .

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The correct Answer is:
`2 sqrt3`
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ARIHANT MATHS-LOGARITHM AND THEIR PROPERTIES-Exercise (Subjective Type Questions)
  1. If log2=0.301 and log3=0.477, find the number of integers in the numb...

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  2. If log2=0.301 and log3=0.477, find the value of log(3.375).

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  3. Find the least value of log2x-logx(0.125)for xgt1 .

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  4. Find values of lamda for which 1/log3lamda+1/log4lamdagt2 .

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  5. Solve the following equations. (i) x^(1+log10x)=10x

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  6. Solve the following equations. (ii)log2(9+2^x)=3

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  7. Solve the following equations. (iii) 2.x^(log(4)3)+3^(log4x)=27

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  8. Solve the following equations. (iv) log4log3log2x=0

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  9. Solve the following equations. (v) x^((log10x+5)/3)=10^(5+log10x)

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  10. Solve the following equations. (vi) log3(log9x+1/2+9^x)=2x

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  11. Solve the following equations. (vii) 4^(log10x+1)-6^(log10x)-2.3^(lo...

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  12. Solve the following equations. (viii) (log10(x-3))/log(10)(x^2-21)=1/...

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  13. Solve the following equations. x^(log2x+4)=32

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  14. Solve the following equations. (x) logax=x, where a=x^(logax)

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  15. Solve the following equations. (xi) log(sqrt2sinx)(1+cosx)=2

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  16. A rational number which is 50 times its own logarithm to the base 10, ...

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  17. [2/log4(2000)^6+3/log5(2000)^6]

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  18. Find the value of x satisfying loga{1+logb{1+logc(1+logpx)}}=0.

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  19. Find the value of 4^(5log(4sqrt2)(3-sqrt6)-6log8(sqrt3-sqrt2)).

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  20. Solve the following inequation . (i) log((2x+3))x^2lt1

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