# Aptitude - Surds and Indices - Discussion

Discussion Forum : Surds and Indices - General Questions (Q.No. 3)
3.
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
Explanation:

xz = y2       10(0.48z) = 10(2 x 0.70) = 101.40

0.48z = 1.40

 z = 140 = 35 = 2.9 (approx.) 48 12

Discussion:
19 comments Page 1 of 2.

Dheeraj verma said:   4 months ago
@All.

Please, can anyone explain in more briefly how we have got 10 (0. 48z) = 10 (2 x 0. 70) = 101. 40?

Zaid Shaikh said:   1 year ago
It's like half (0.48) z is 1.40 then full z (0.96) 2.80 therefore 1 Z is 2.9.
(4)

Monisha Mohanan said:   3 years ago
X^ z = y ^ 2
[10^ .048]^z = [10 ^0.70]^2
Taking log on both sides,
Log [10^ .048]^z = log [10 ^0.70]^2

Log a^b^c = c log a^ b
And similarly c log a^b = c*b log a

Z log10^ .048 = 2 log 10 ^0.70
Z * .48 log 10 = 2 * 0.70 log 10

.48 z = 1.4 here log 10 = 1.
Z = 1.4 /.48.

For easy calculation multiplying it by 100,
Z = 140/48 = 2.9.

Naman said:   4 years ago
I cannot understand it.
(1)

Jesophat said:   5 years ago
48/100 = 0.48z =1.4z.

Akhila said:   6 years ago
@Jaichu.

For both nums decimal at the same place. So, a decimal can be removed.

Aniket Gaikwad said:   7 years ago
Thanks @Tulasi.

Jaichu said:   7 years ago

0.48z = 1.40.
z =140/48.

How could they multiply it?

Thiyaguaxrev4fvtr said:   8 years ago