Home
Class 12
MATHS
10^(logp(logq(logr(x))))=1 and logq(logr...

`10^(log_p(log_q(log_r(x))))=1` and `log_q(log_r(log_p(x)))=0` then 'p' equals

A

`r^(q//r)`

B

`rq`

C

1

D

`r^(r//q)`

Text Solution

Verified by Experts

`log_(p)log_(q)log_(r)x=0`
`{:(log_(q)log_(r)x=1,log_(r)log_(p)x=1),(log_rx=q,log_(p)x=r),(x=r^q...(1),x=p^(r)...(2)):}`
By equation (1) and (2) `p=r^(q//r)`
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    BANSAL|Exercise Physics, SECTION-1 (PART-A)|5 Videos

  • TEST PAPERS

    BANSAL|Exercise Physics, SECTION-1 (PART-A) [COMPREHENSION TYPE]|2 Videos

  • TEST PAPERS

    BANSAL|Exercise Math|15 Videos

  • PROBABILITY

    BANSAL|Exercise All Questions|1 Videos

  • THERMODYNAMICS

    BANSAL|Exercise Match the column|7 Videos

Similar Questions

Explore conceptually related problems

10^(log_p(log_q(log_r(x))))=1 and log_q(log_r(log_p(x)))=0, then 'p' is equals a. r^(q/r) b. rq c. 1 d. r^(r/q)

If 10^(log_a(log_b(log_c x)))=1 and 10^((log_b(log_c(log_a x)))=1 then, a is equal to

IF 10^(log_p{log_q(log_rx)}) =1 and log _q{log_r(log_px)}=0 . The value of q is

IF 10^(logp{logq(logr^x)}) =1 and log _q{log_r(log_px)}=0 . The value of x is

log_(a)(mnp)=log_(a)m+log_(a)n+log_(a)p

log_(a)((P)/(Q))=log_(a)P-log_(a)Q

Q.If log_(x)a,a^((x)/(2)) and log_(b)x are in G.P.then x is equal to (1)log_(a)(log_(b)a)(2)log_(a)(log_(e)a)+log_(a)log_(b)b(3)-log_(a)(log_(a)b)(4) none of these

If log2,log(2^(x)-1) and log(2^(x)+3) are in A.P.then x is equal to

If log_(x)y= (log_(a)y)/(P) then the value of P is

BANSAL-TEST PAPERS-MATHS
  1. (sqrt2-sin25^(@)-cos25^(@))/(sin25^(@)-cos25^(@)) is equal to

    Text Solution

    |

  2. The value of (1+cos ""(2pi)/(15))(1+cos""(8pi)/(15))(1+cos""(12pi)/...

    Text Solution

    |

  3. 10^(logp(logq(logr(x))))=1 and logq(logr(logp(x)))=0 then 'p' equals

    Text Solution

    |

  4. For 0ltalphaltbetalt(pi)/(2),if(sinalpha)/(sinbeta)=(sqrt3)/(2)and (c...

    Text Solution

    |

  5. The equation (log)(x^2)\ 16 + (log)(2x)64=3\ h a s one irrational ...

    Text Solution

    |

  6. If A=sum(r=7)^(2400)log(7)((r+1)/(r))," "B=prod(r=2)^(1023) log(r)(t+...

    Text Solution

    |

  7. If y=log(7-a)(2x^(2)+2x+a3)"is defined"AAx inR, then possible integral...

    Text Solution

    |

  8. Match the following Column I to Column II

    Text Solution

    |

  9. Match the following Column I to Column II

    Text Solution

    |

  10. If (n,theta)=prod(n=1)^(n)((1+tan^(2)(2""^(n)theta))/((1-tan^(2)(2""^(...

    Text Solution

    |

  11. Find the number of integral solution of the equation (log)(sqrt(x))...

    Text Solution

    |

  12. Find the number of integral ordered pairs (x,y) satisfying the equatio...

    Text Solution

    |

  13. If sin beta=sin(2alpha+beta) then find the value of (cotalpha+cot(alph...

    Text Solution

    |

  14. If a = log245 175 and b = log1715 875, then the value of (1-ab)/(a-b) ...

    Text Solution

    |

  15. If P=x+1/x and P(tan alpha)=2, P(tan beta)=2sqrt2, P(cot gamma)=4 wher...

    Text Solution

    |

  16. A die is rolled thrice, find the probability of getting a larger nu...

    Text Solution

    |

  17. The value of Sigma(i=1)^(6) (sin .(2pik)/(7)-i cos .(2pik)/(7))

    Text Solution

    |

  18. Find the eccentricity of an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 whose la...

    Text Solution

    |

  19. AB is double ordinate of the hyperbola x^2/a^2-y^2/b^2=1 such that Del...

    Text Solution

    |

  20. The curve described parametrically by x = t^2 + t +1, y = t^2 - t + 1 ...

    Text Solution

    |