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:
Answer: Option
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:
20 comments Page 1 of 2.
Monisha Mohanan said:
4 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.
[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.
(1)
Tulasi said:
10 years ago
10^0.48 = x //given.
10^0.7 = y //given.
x^z = (10^0.7)^2.
Since (a^m)^n = a^(m*n) we get,
(10^0.48)^z = 10^(z*0.48) and (10^0.7)^2 = 10^(0.7*2).
Now, 10^(0.48*z) = 10^(0.7*2).
Since bases are equal, equating powers we get:
z*0.48 = 0.7*2.
z = 140/48.
z = 2.9166 which is approximately 2.9.
10^0.7 = y //given.
x^z = (10^0.7)^2.
Since (a^m)^n = a^(m*n) we get,
(10^0.48)^z = 10^(z*0.48) and (10^0.7)^2 = 10^(0.7*2).
Now, 10^(0.48*z) = 10^(0.7*2).
Since bases are equal, equating powers we get:
z*0.48 = 0.7*2.
z = 140/48.
z = 2.9166 which is approximately 2.9.
Sagar said:
1 decade ago
It is very easy to solve if you know Logarithm.
Step1: Zlog(10^0.48)=2log(10^0.70)
Step2: ZX0.48=2X0.70 (Log10=1)
Step3: Z= 2.9
Step1: Zlog(10^0.48)=2log(10^0.70)
Step2: ZX0.48=2X0.70 (Log10=1)
Step3: Z= 2.9
Dheeraj verma said:
2 years ago
@All.
Please, can anyone explain in more briefly how we have got 10 (0. 48z) = 10 (2 x 0. 70) = 101. 40?
Please, can anyone explain in more briefly how we have got 10 (0. 48z) = 10 (2 x 0. 70) = 101. 40?
(1)
Vignesh said:
1 decade ago
This not the different one, as like a to the power m whole to the power of n=a to the power of m*n.
Adeyemi Raphael said:
1 decade ago
Why do both side have to divided, not addtion, subtraction or mutplication to get final answer?
Nego said:
1 decade ago
I'm a bit confused about this. Why is the y2 not (0.70*0.70), rather its (2*0.70)?
Akhila said:
7 years ago
@Jaichu.
For both nums decimal at the same place. So, a decimal can be removed.
For both nums decimal at the same place. So, a decimal can be removed.
Rajesh said:
1 decade ago
Its very Simple. If Base Values are equal of both side than power's are equal.
Zaid Shaikh said:
3 years 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)
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