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if (a+log4 3)/(a+log2 3)= (a+log8 3)/(a+...

if `(a+log_4 3)/(a+log_2 3)= (a+log_8 3)/(a+log_4 3)=b` then find the value of `b`

A

`1/2`

B

`2/3`

C

`1/3`

D

`3/2`

Text Solution

Verified by Experts

The correct Answer is:
C
`(a+log_(4) 3)/(a+log_(2)3) = (a+log_(8) 3)/(a+log_(4)3) = (log_(4) 3-log_(8) 3)/(log_(2)3-log_(4) 3) = 1/3`
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CENGAGE-LOGARITHM AND ITS PROPERTIES-Exercise (Single)
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  2. If a, b, c are consecutive positive integers and log (1+ac) = 2K, then...

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  3. if (a+log4 3)/(a+log2 3)= (a+log8 3)/(a+log4 3)=b then find the value ...

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  5. The value of (1+2(log3 2)/((1+(log)3 2)^2)+((log)6 2)^2 is 2 (b) 3 (...

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  6. If (log)4 5=aa n d(log)5 6=b , then (log)3 2 is equal to 1/(2a+1) (b)...

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  7. If log(10) 2 = a, log(10)3 = b" then "log(0.72)(9.6) in terms of a an...

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  8. There exists a natural number N which is 50 times its own logarithm to...

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  9. The value of ((log)2 24)/((log)(96)2)-((log)2 192)/((log)(12)2) is

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  10. log(x-1)x*log(x-2)(x-1)*...*log(x-12)(x-11) = 2,x is equal to

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  11. If f.(x)= log((1+x)/(1-x)), then

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  12. If a^4b^5=1 then the value of loga(a^5b^4) equals

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  13. The value of 3^((log)4 5)-5^((log)4 3) is 0 (b) 1 (c) 2 (d) none of...

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  14. If 2^(x+y) = 6^(y) and 3^(x-1) = 2^(y+1), then the value of (log 3 - l...

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  15. The value of x satisfying sqrt3^(-4+2log(sqrt5)x)= 1//9 is

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  16. The value of x satisfying the equation root(3)(5)^(log(5)5^(log(5)5^...

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  17. If sqrt((log)2x)-0. 5=(log)2sqrt(x ,) then x equals

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  18. If log(y) x + log(x) y = 2, x^(2)+y = 12 , then the value of xy is

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  19. 4^(log9 3)+9^(log2 4)=1 0^(logx 83), then x is equal to

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  20. Solve (x+1)^(log(10) (x+1))=100(x+1)

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