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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-LOGARITHM AND ITS PROPERTIES-Exercise (Single)
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  2. The value of x satisfying sqrt3^(-4+2log(sqrt5)x)= 1//9 is

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

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

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  6. 4^(log9 3)+9^(log2 4)=1 0^(logx 83), then x is equal to

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

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  12. The equation log4(2-x)+log(0.25)(2+x)=log4(1-x)+log(0.25)(2x+1) has

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  14. If the equation 2^x+4^y=2^y is solved for y in terms of x where x<0, t...

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

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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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  20. Number of real values of x satisfying the equation (log)2(x^2-x)(log)...

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