Aptitude - Logarithm - Discussion
Discussion Forum : Logarithm - General Questions (Q.No. 12)
12.
| If logx |  |
9 |  |
= - | 1 | , then x is equal to: |
| 16 | 2 |
Answer: Option
Explanation:
| logx | |
9 | |
= - | 1 |
| 16 | 2 |
 x-1/2 |
= | 9 |
| 16 |
| |
1 | = | 9 |
| x | 16 |
| x = |
16 |
| 9 |
| x = |
|
16 | |
2 |
| 9 |
| x = |
256 |
| 81 |
Discussion:
17 comments Page 1 of 2.
J. Bhargav sai said:
4 years ago
This is also correct answer.
Log x (9/16) = -1/2,
Log x (3/4)^2 = -1/2,
Log x^ (-1/2) = (3/4) ^2,
√x = (3/4) ^2.
Root and square both cancel.
And after x = (3/4).
X = (3/4),
Log x (9/16) = -1/2,
Log x (3/4)^2 = -1/2,
Log x^ (-1/2) = (3/4) ^2,
√x = (3/4) ^2.
Root and square both cancel.
And after x = (3/4).
X = (3/4),
(2)
PAVITHRA_228 said:
10 years ago
As per the formula.
log x = m.
=> log x/log a = m.
=> log (9/16)/log a = -1/2.
=>2 log (9/16) = -log a.
=> log (9/16)^2 = log(1/a).
=> log (81/256) = log(1/a).
log gets cancelled,
=> a = 256/81.
log x = m.
=> log x/log a = m.
=> log (9/16)/log a = -1/2.
=>2 log (9/16) = -log a.
=> log (9/16)^2 = log(1/a).
=> log (81/256) = log(1/a).
log gets cancelled,
=> a = 256/81.
(2)
Carbon said:
1 decade ago
A far better solution can be done just by observation,
Just multiply both side by -(1/2) to make RHS.
Then simplifying LHS we get,
Logx(9/16) pow(-1/2).
= logx(256/81) = 1.
Thus,
X=256/81.
Just multiply both side by -(1/2) to make RHS.
Then simplifying LHS we get,
Logx(9/16) pow(-1/2).
= logx(256/81) = 1.
Thus,
X=256/81.
(1)
Rohit said:
1 decade ago
loga(9/16)=-1/2
log(9/16)/loga=-1/2
2log(9/16)=-loga
log(81/256)=log(1/a)
a=256/81
log(9/16)/loga=-1/2
2log(9/16)=-loga
log(81/256)=log(1/a)
a=256/81
(1)
Kathir said:
9 years ago
@Rohit. Good explanation.
Deepanesh said:
5 years ago
Log X = m.
X = 9/16.
m = -1/2,
a power m = X ->Formula.
X = 9/16.
m = -1/2,
a power m = X ->Formula.
Nagaraju Azmeera said:
5 years ago
Thanks for explaining @Pavitra.
Xcpen said:
7 years ago
X^-1/2 = 9/16,
1/x^1/2 = 9/16,
1/x^1/2 = (3/4)^1/2,
1/x = 3/4,
X = 4/3.
1/x^1/2 = 9/16,
1/x^1/2 = (3/4)^1/2,
1/x = 3/4,
X = 4/3.
Himansu said:
8 years ago
log(0.1)=-1/3.
Multiplying LHS and RHS by -3 we get,
RHS = 1 and,
LHS = -3 logx(1/10),
= logx (10) to power 3,
= logx (1000)=1,
x = 1000.
Multiplying LHS and RHS by -3 we get,
RHS = 1 and,
LHS = -3 logx(1/10),
= logx (10) to power 3,
= logx (1000)=1,
x = 1000.
Rushikesh said:
9 years ago
@ Mounika.
X = 2.15.
X = 2.15.
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