Home
Class 9
MATHS
If a = b^(2x) , b = c^(2y) and c = a^(2z...

If a = `b^(2x) , b = c^(2y) and c = a^(2z)`, show that 8xyz = 1.

Text Solution

Verified by Experts

The correct Answer is:
8xyz = 1
Promotional Banner

Topper's Solved these Questions

  • INDICES [EXPONENTS]

    ICSE|Exercise EXERCISE 7 (A)|23 Videos

  • INDICES [EXPONENTS]

    ICSE|Exercise EXERCISE 7 (B)|29 Videos

  • INDICES (EXPONENTS)

    ICSE|Exercise 4 Marks Questions|9 Videos

  • INEQUALITIES

    ICSE|Exercise EXERCISE 11|42 Videos

Similar Questions

Explore conceptually related problems

Statement-1: If a =y^(2), b=z^(2) " and " c= x^(2), " then log"_(a) x^(3) xx "log"_(b) y^(3) xx "log"_(c)z^(3) = (27)/(8) Statement-2: "log"_(b) a = (1)/("log"_(a)b)

If x^(a) = y^(b) = z^ (c ) and y^(2) = xz, prove that b= ( 2ac)/( a+c)

If a^x=b^y=c^z and b^2=a c , then show that y=(2z x)/(z+x)

If a^x=b^y=c^z and a,b,c are in G.P. show that 1/x,1/y,1/z are in A.P.

If x = a sec A cos B, y = b sec A sin B and z = c tan A, show that : (x^(2))/ (a^(2)) + (y^(2))/ (b^(2)) - (z^(2))/(c^(2)) = 1

If a, b, and c are not equal to 0 or 1 and if a^x = b, b^y = c and c^x = a then xyz =

A triangle has its three sides equal to a , b and c . If the coordinates of its vertices are A(x_1, y_1),B(x_2,y_2) \ a n d \ C(x_3,y_3), show that |[x_1,y_1, 2],[x_2,y_2, 2],[x_3,y_3, 2]|^2=(a+b+c)(b+c-a)(c+a-b)(a+b-c)

If the origin lies in the acute angle between the lines a_1 x + b_1 y + c_1 = 0 and a_2 x + b_2 y + c_2 = 0 , then show that (a_1 a_2 + b_1 b_2) c_1 c_2 lt0 .

If a^2+b^2+c^2=x^2+y^2+z^2=1, then show that a x+b y+c z leq1.

If a^x=b^y=c^z\ a n d\ b^2=a c , prove that y=(2x z)/(x+z)

ICSE-INDICES [EXPONENTS]-EXERCISE 7 (C)
  1. If a = b^(2x) , b = c^(2y) and c = a^(2z), show that 8xyz = 1.

    Text Solution

    |

  2. Evaluate : 9^((5)/(2)) - 3xx8^(0)-((1)/(81))^(-(1)/(2))

    Text Solution

    |

  3. Evaluate : (64)^((2)/(3))-root(3)(125)-(1)/(2^(-5))+(27)^(-(2)/(3))...

    Text Solution

    |

  4. Evaluate : [(-(2)/(3))^(-2)]^(3)xx((1)/(3))^(-4)xx3^(-1)xx(1)/(6)

    Text Solution

    |

  5. Simplify : (3xx9^(n+1)-9xx3^(2n))/(3xx3^(2n+3)-9^(n+1))

    Text Solution

    |

  6. Solve : 3^(x-1)xx5^(2y-3)=225.

    Text Solution

    |

  7. If ((a^(-1)b^(2))/(a^(2)b^(-4)))div((a^(3)b^(-5))/(a^(-2)b^(3)))=a^(x)...

    Text Solution

    |

  8. If 3^(x +1) = 9^(x - 3), find the value of 2^(1 + x).

    Text Solution

    |

  9. If 2^(x)=4^(y)=8^(z) and (1)/(2x)+(1)/(4y)+(1)/(8z)=4 find the value o...

    Text Solution

    |

  10. If (9^n\ x\ 3^2\ x\ 3^n-\ 27^n)/(3^(3m)\ x\ 2^3)=1/(27) , prove that m...

    Text Solution

    |

  11. Solve for x : x:(13)^sqrt(x)=4^(4)-3^(4)-6.

    Text Solution

    |

  12. If 3^(4x)=(81)^(-1)and(10)^((1)/(y))=0.0001, value of 2^(-x) xx 16^(y)...

    Text Solution

    |

  13. Solve the equation: 3(2^x+1)-2^(x+2)+5=0

    Text Solution

    |

  14. If (a^(m))^(n)=a^(m).a^(n), find the value of : m(n - 1) - (n - 1)

    Text Solution

    |

  15. If m = root(3)(15) and n = root(3)(14), find the value of m - n - (1)/...

    Text Solution

    |

  16. Evaluate : (2^(n)xx6^(m+1)xx10^(m-n)xx15^(m+n-2))/(4^(m)xx3^(2m+n)xx25...

    Text Solution

    |

  17. Evaluate : ((x^(q))/(x^(r )))^((1)/(qr))xx((x^(r ))/(x^(p)))^((1)/(rp)...

    Text Solution

    |

  18. Prove that: (a^(-1))/(a^(-1)+b^(-1))+(a^(-1))/(a^(-1)-b^(-1))=(2b^2)/(...

    Text Solution

    |

  19. Prove that: (a+b+c)/(a^(-1)\ b^(-1)+b^(-1)\ c^(-1)+c^(-1)a^(-1))=a b c

    Text Solution

    |

  20. Evaluate : (4)/((216)^(-2//3))+(1)/((256)^(-3//4))+(2)/((343)^(-1//3)...

    Text Solution

    |