# Surds and Indices

## Surds and Indices

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Question 1 |

(17)^3.5 x (17)^? = 17^8

2.29 | |

2.75 | |

4.25 | |

4.5 |

Question 1 Explanation:

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

Question 2 |

Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to:

1.45 | |

1.88 | |

2.9 | |

3.7 |

Question 2 Explanation:

x^z = y^2 10^(0.48z) = 10^(2 x 0.70) = 10^(1.40)
0.48z = 1.40
z =140/48 =35/12 =2.9 (approx.)

Question 3 |

If 5^a = 3125, then the value of 5^(a - 3) is:

25 | |

125 | |

625 | |

1625 |

Question 3 Explanation:

5^a = 3125 5^a = 5^5
a = 5.
5^(a - 3) = 5^(5 - 3) = 5^2 = 2^5.

Question 4 |

If 3^(x - y) = 27 and 3^(x + y) = 243, then x is equal to:

0 | |

2 | |

4 | |

6 |

Question 4 Explanation:

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.

Question 5 |

(256)0.16 x (256)0.09 = ?

4 | |

16 | |

64 | |

256.25 |

Question 5 Explanation:

(256)^0.16 x (256)^0.09 = (256)^(0.16 + 0.09) ==> (256)^0.25b==> (256)^(25/100) ==> 4^(4*(1/4))1/4)=4

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