# Aptitude - Surds and Indices

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- Surds and Indices - Formulas
- Surds and Indices - General Questions

^{3.5}x (17)

^{?}= 17

^{8}

Let (17)^{3.5} x (17)^{x} = 17^{8}.

Then, (17)^{3.5 + x} = 17^{8}.

3.5 + *x* = 8

*x* = (8 - 3.5)

*x* = 4.5

If | a |
x - 1 |
= | b |
x - 3 |
, then the value of x is: |
||||

b |
a |

Given | a |
x - 1 |
= | b |
x - 3 |
|||

b |
a |

a |
x - 1 |
= | a |
-(x - 3) |
= | a |
(3 - x) |
|||||||

b | b | b |

*x* - 1 = 3 - *x*

2*x* = 4

*x* = 2.

^{0.48}=

*x*, 10

^{0.70}=

*y*and

*x*

^{z}=

*y*

^{2}, then the value of

*z*is close to:

*x*^{z} = *y*^{2} 10^{(0.48z)} = 10^{(2 x 0.70)} = 10^{1.40}

0.48*z* = 1.40

z = |
140 | = | 35 | = 2.9 (approx.) |

48 | 12 |

^{a}= 3125, then the value of 5

^{(a - 3)}is:

5^{a} = 3125 5^{a} = 5^{5}

*a* = 5.

5^{(a - 3)} = 5^{(5 - 3)} = 5^{2} = 25.

^{(x - y)}= 27 and 3

^{(x + y)}= 243, then

*x*is equal to:

3^{x - y} = 27 = 3^{3} *x* - *y* = 3 ....(i)

3^{x + y} = 243 = 3^{5} *x* + *y* = 5 ....(ii)

On solving (i) and (ii), we get *x* = 4.