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Prove that log(10) 2" lies between " 1/...

Prove that ` log_(10) 2" lies between " 1/4 and 1/3`.

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The correct Answer is:
`3 lt 12` `log_(10)2lt4implies 1/4ltlog_(10)2lt1/3`
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ARIHANT MATHS-LOGARITHM AND THEIR PROPERTIES-Exercise (Subjective Type Questions)
  1. If (Ina)/(b-c)=(Inb)/(c-a)=(Inc)/(a-b), prove the following . a^a+b^b...

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  2. If (Ina)/(b-c)=(Inb)/(c-a)=(Inc)/(a-b), prove the following . a^(b^2+...

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  3. Prove that log(10) 2" lies between " 1/4 and 1/3.

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  4. If log2=0.301 and log3=0.477, find the number of integers in 5^(200)

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  5. If log2=0.301 and log3=0.477, find the number of integers in 6^(20)

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  6. If log2=0.301 and log3=0.477, find the number of integers in the numb...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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