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If (log)(10)2=a ,(log)(10)3=bt h e n(log...

If `(log)_(10)2=a ,(log)_(10)3=bt h e n(log)_(0. 72)(9. 6)` in terms of `aa n db` is equal to `(2a+3b-1)/(5a+b-2)` (b) `(5a+b-1)/(3a+2b-2)` (c) `(3a+b-2)/(2a+3b-1)` `(2a+5b-2)/(3a+b-1)`

A

`(2a+3b-1)/(5a+b-2)`

B

`(5a+b-1)/(3a+2b-2)`

C

`(3a+b-2)/(2a+3b-1)`

D

`(2a+5b-2)/(3a+b-1)`

Text Solution

Verified by Experts

The correct Answer is:
B
`log_(0.72)(9.6)= log_(72/100)(96/10) =((log_(10) 96-log_(10) 10))/((log_(10) 72 - log_(10)100))`
`=(log_(10)(2^(5)xx3)-1)/(log_(10)(2^(3)xx3^(2))-2)`
`=(5a+b-1)/(3a+2b-2)`
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CENGAGE-LOGARITHM AND ITS PROPERTIES-Exercise (Single)
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  2. 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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  3. If (log)(10)2=a ,(log)(10)3=bt h e n(log)(0. 72)(9. 6) in terms of aa ...

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

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  5. The value of ((log)2 24)/((log)(96)2)-((log)2 192)/((log)(12)2) is 3 (...

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  6. (log)(x-1)x (log)(x-2)(x-1) (log)(x-12)(x-11)=2,x is equal to: 9 (b) ...

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  7. If f(x)=log((1+x)/(1-x)),t h e n f(x1)f(x)=f(x1+x2) f(x+2)-2f(x+1)...

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  8. about to only mathematics

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

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  10. If 2^(x+y)=6^ya n d3^(x-1)=2^(y+1), then the value of (log3-log2)(x-y)...

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

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  12. The value of x satisfying the equation 3sqrt(5)^(log)5 5^(((log)5(log)...

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  13. If sqrt((log)2x)-0. 5=(log)2sqrt(x ,) then x equals odd integer (b)...

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  14. if (log)y x+(log)x y=1,x^2+y=12 , the value of x y is 9 (b) 12 (c) 15 ...

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  15. 4^(log9 3)+9^(log2 4)=1 0^(logx 83), then x is equal to

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  16. If (x+1)^((log)(10)(x+1))=100(x+1), then

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  17. If log2x+logx2=10/3=log2y+logy2 and x!=y ,then x+y=

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  18. If (log)(10)[1/(2^x+x-1)]=x[(log)(10)5-1] , then x= 4 (b) 3 (c) 2 ...

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  19. If (log)3{5+4(log)3(x-1)}=2, then x is equal to 4 (b) 3 (c) 8 (d) (...

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  20. If 2x^((log)4 3)+3^((log)4x)=27 , then x is equal to 2 (b) 4 (c) 8 (d...

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