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Quantitative Ability Tech Test Logarithms Test 2

44100.If $\log_{10}{7}=a, then \log_{10}({\frac{1}{70}}) $is equal to:
-(1+a)
$(1+a)^{-1}$
$\frac{a}{10}$
$\frac{1}{10a}$
Explanation:

$\log_{10}({\dfrac{1}{70}})$= $\log_{10}{1}- \log_{10}{70}$
=>$- \log_{10}{7\times 10}$
=>-(a+1)
44101.$\log_{10}{5}+\log_{10}{5x+1}=\log_{10}{(x+5)}+1$,then x is equal to:
1
3
5
10
Explanation:

$\log_{10}{5}+\log_{10}{(5x+1)}$=$\log_{10}{(x+5)}+1$
=>$\log_{10}{5}+\log_{10}{(5x+1)}$=$\log_{10}{(x+5)}+\log_{10}{10}$
=>$\log_{10}{5(5x+1)}$
=>$\log_{10}{10(x+5)}$
=>5(5x+1)=10(x+5)
=>5x+1=2x+10
=>3x=9
=>x=3
44104.The value of $\left(\frac{1}{\log_{3}{60}}+\frac{1}{\log_{4}{60}}+\frac{1}{\log_{5}{60}}\right) is:$
0
1
5
60
Explanation:

Given expression:
$\log_{60}{3}+\log_{60}{4}+\log_{60}{5}$
=>$\log_{60}{(3\times 4\times 5)}$
=>$\log_{60}{60}$
=1.
44106.The value of $\log{2}{16}$ is
$\dfrac{1}{8}$
4
8
16
Explanation:

Let $\log{2}{16}$=n.
then,$2^{n}$=16=$2^{4}$=>n=4
Therefore ,$\log{2}{16}$=4
44108.If $log \dfrac{a}{b}+log \dfrac{b}{a}$=log(a+b),then
a + b = 1
a - b = 1
a = b
$a^{2}-b^{2}=1$
Explanation:

$log \dfrac{a}{b}+log \dfrac{b}{a}$=log(a+b)
=>log(a+b)=$log(\dfrac{a}{b} \times \dfrac{b}{a})$=log 1.
so,a+b=1
44417.If $log_{2}[log_{3}(log_{2} x)]$ = 1, x is equal to:
512
None of these
256
1024
Explanation:

$log_{2}[log_{3}(log_{2} x)]$ = 1

=>$log_{2}[log_{3}(log_{2} x)]$ = $log_{2}(2)$

=> $log_{3}(log_{2} x)$=2

=>$log_{2} x$=$3^2$=9

=> x = $2^9$ = 512

44423.The value of $\dfrac{1}{log_{xy}xyz}+\dfrac{1}{log_{yz}xyz}+\dfrac{1}{log_{zx}xyz}$ is
1
2
log 2
$\dfrac{1}{2}$
Explanation:

$\dfrac{1}{log_{xy}xyz}+\dfrac{1}{log_{yz}xyz}+\dfrac{1}{log_{zx}xyz}$

= $log_{xyz} xy + log_{xyz} yz + log_{xyz} zx$

=$log_{xyz}(xy \times yz \times zx)$

=$log_{xyz}(xyz)^{2}$

= $2log_{xyz}xyz$

= 2 x 1

= 2

44424.If $log_{a}b$ =$\dfrac{1}{2}, log_{b}c$ =$\dfrac{1}{3}\:and\: log_{c}a$ =$\dfrac{k}{5}$, the value of k is
25
35
30
20
Explanation:

$log_{a}b$ =$\dfrac{log\:b}{log\:a}, log_{b}c$ =$\dfrac{log\:c}{log\:b}, log_{c}a$ =$\dfrac{log\:a}{log\:c}$

$log_{a}b \times log_{b}c \times log_{c}a$ =$\dfrac{log\:b}{log\:a}\times\dfrac{log\:c}{log\:b}\times\dfrac{log\:a}{log\:c}$=$\dfrac{1}{2}\times\dfrac{1}{3}\times\dfrac{k}{5}$

=>1=$\dfrac{k}{30}$

=>k = 30

44425.The value of log 9/8 - log 27/32 + log3/4 is ?
0
1
2
3
Explanation:

Given Exp. = log [{(9/8) / (27/32)} x 3/4)]

= log [(9/8) x (3/4) x (32/27)]

= log 1

= 0

44426.If $log_{5} (x^2 + x) - log_{5} (x + 1)$ = 2, then the value of x is
30
25
10
5
Explanation:

$log_{5}\left(\dfrac{x^2+x}{x+1}\right)$=$log_{5}25$

=>$\left(\dfrac{x^2+x}{x+1}\right)$=25

=>$x^2-24x-25$=0

=>$(x-25)(x+1)$=0

=>x=25

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