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Solve the following equations. (x) loga...

Solve the following equations.
(x) `log_ax=x`, where `a=x^(log_ax)`

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The correct Answer is:
x=1
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ARIHANT MATHS-LOGARITHM AND THEIR PROPERTIES-Exercise (Subjective Type Questions)
  1. Solve the following equations. (viii) (log10(x-3))/log(10)(x^2-21)=1/...

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

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

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

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

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

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

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

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

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  10. Solve the following inequation . (ii) log(2x)(x^2-5x+6)lt1

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  11. Solve the following inequation . (iii) log(2)(2-x)ltlog(1//2)(x+1)

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  12. Solve the following inequation . (iv) log(x^2)(x+2)lt1

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  13. Solve the following inequation . (v) 3^(log3sqrt((x-1)))lt3^(log3(x-...

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  14. Solve the following inequation . (vi) log(1//2)(3x-1)^2ltlog(1//2)(x...

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  15. Solve the following inequation . (vii) log(10)x+2lelog10^2x

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  16. Solve the following inequation . (viii) log10(x^2-2x-2)le0

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  17. Solve the following inequation . (ix) logx(2x-3/4)gt2

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  18. Solve the following inequation . log(1//3)xltlog(1//2)x

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  19. Solve the inequation log(2x+3)x^(2)ltlog(2x+3)(2x+3)

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  20. Solve the following inequation . (xii) log2^2x+3log2xge5/2log(4sqrt2...

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