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The value of x satisfying the equation ...

The value of x satisfying the equation
`root(3)(5)^(log_(5)5^(log_(5)5^(log_(5)5^(log_(5)((x)/(2))`= 3, is

A

1

B

3

C

18

D

54

Text Solution

Verified by Experts

The correct Answer is:
D
Using ` a^(log_(a)N) = N` repeatedly, we get
`(root(3)5)^(log _(5)(x/2)) = 3`
`rArr 5^(log_(5)(x/2)^(1//3)) = 3`
`rArr (x/2)^(1//3)= 3`
` rArr x/2 = 27`
`rArr x = 54`
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CENGAGE ENGLISH-LOGARITHM AND ITS PROPERTIES-Exercises (Single Correct Answer Type)
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  7. Solve (x+1)^(log(10) (x+1))=100(x+1)

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

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

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  11. If 2x^(log(4)3)+3^(log(4)x)= 27, then x is equal to

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  14. If the equation 2^x(1-2^x)+4^y=2^y is solved for y in terms of x where...

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  15. The number of solution of x^(log(x)(x+3)^(2)) = 16is

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  16. The product of roots of the equation (log(8)(8//x^(2)))/((log(8)x)^(2)...

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  17. Let agt1 be a real number . If S is the set of real number x that are...

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  18. the number of roots of the equation log(3sqrtx) x + log(3x) (sqrtx) =0...

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  19. The set of all x satisfying the equation x^(log)3x^2+((log)3x)^(2-10)=...

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