The value of $ \frac{\log_{a}{x}}{\log_{ab}{x}} - \log_{a}{b}$ is? 0 1 a ab ? lo

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Question
The value of $ \frac{\log_{a}{x}}{\log_{ab}{x}} - \log_{a}{b}$ is?
Options
A. 0
B. 1
C. a
D. ab

Correct Answer

1

Explanation

? log_a x = ( log_abx) / (log_aba)
? The given expression = [[(log_abx) / (log_aba)] / [( log_abx )] - ( log_ab)
= (1/log_aba) - log_ab = log_aab - log_ab = log_a(ab/b)
= log_aa = 1

Logarithm problems

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1.
If log 2 = 0.3010, then the number of digits in 2 ⁶⁴ is?
Options
A. 18
B. 19
C. 20
D. 21

2.
Two poles of ht. a and b meters are p meters apart ( b > a). The height of the point of intersection of the lines joining the top of each pole to the foot of the opposite pole is :
Options
A. a+b ab
B. p a+b
C. ab a+b
D. a+b p

3.
In the fig. XY || AC and XY divides triangular region ABC into two part equal in area.

Then AX is equal to :

AB
Options
A. 1 ?2
B. ?2 + 2 ?2
C. 1 2
D. ?2 - 2 ?2

4.
In a ? ABC, the bisectors of ? B and ? C intersect each other at a point O. Then ? BOC is equal to :
Options
A. 90 � - 1 ?A 2
B. 120� + 1 ?A 2
C. 90 � + 1 ?A 2
D. 120� - 1 ?A 2

5.
In a ? ABC, the sides AB and AC are produced to P and Q respectively. The bisectors of ? OBC and ? QCB intersect at a point O. Then ? BOC is equal to:
Options
A. 90 � + 1 ?A 2
B. 90 � - 1 ?A 2
C. 120� + 1 ?A 2
D. 120� - 1 ?A 2

6.
The value of log ₂3 x log ₃2 x log ₃4 x log ₄3 is?
Options
A. 1
B. 2
C. 3
D. 4

7.
Given that log ₁₀ 2 = 0.3010, then log ₂ 10 is equal to?
Options
A. 0.3010
B. 0.6990
C. 1000 / 301
D. 699 / 301

8.
The value of log 9/8 - log 27/32 + log3/4 is?
Options
A. 0
B. 1
C. 2
D. 3

9.
The simplified form of log(75/16) -2 log(5/9) +log(32/343) is?
Options
A. log 2
B. 2 log 2
C. log 3
D. log 5

10.
If log 2 = 0.3010 then log 5 equals to?
Options
A. 0.3010
B. 0.6990
C. 0.7525
D. Given log 2, it is not possible to calculate log 5

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