Standard Logarithm

Q.

If a=$lo{g}_{12}18$, b=$lo{g}_{24}54$ then the value of ab+5(a-b) is

1. 0

2. 1

3. None of these

4. 4

Q.

If $a,b,c$ are three consecutive integers, then $log(1+ac)$ is ________ .

1. log abc

2. 2 log a

3. 2 log b

4. log b

Q.

100√25÷√25+x =50 then find the value of x

Q.

$lo{g}_2\left(2\right)$ is equal to _______ .

___

Q. If $a^2+4b^2=12ab$, then log(a + 2b) is

1. $\frac{1}{2}[loga+logb+4log2]$
2. $\frac{1}{2}[loga+logb-log2]$
3. $\frac{1}{2}[loga-logb+4log2]$
4. $log\frac{a}{2}+log\frac{b}{2}+log2$

Q. If ${\log }_{10}2=0.3010$ & ${\log }_{10}3=0.4771$, then the value of ${\log }_{10}\left(2.25\right)$ is

1. $0.3522$
2. $0.3532$
3. $0.3265$
4. $0.3256$

Q. $7log\left(\frac{16}{15}\right)+5log\left(\frac{25}{24}\right)+3log\left(\frac{81}{80}\right)$ is equal to

1. 0
2. 1
3. log 2
4. log 3

Q. If ${\log }_5(x-7)=1$, then value of $x$ is equal to

1. $12$
2. $13$
3. $14$
4. $15$

Q. Find the value of ${\log }_{\sqrt{2}}64.$

Q. If $\left(a^{mn}\right)=a^m-a^n$, find the value of $m(n-1)-(n-1)$.

1. $1$
2. $2$
3. $3$
4. $0$

Q. The value of ${\log }_{0.5}16$ is equal to

1. $-4$
2. $-1$
3. $-2$
4. $0$

Q. Determine the value of $3^{2-\log \frac{6}{3}}$

Q. If ${\log }_{3x+5}(a{x}^2+8x+2)>2$ then $x$ lies in the interval:

1. $(-\frac{4}{3},-\frac{20}{11})$
2. $(-\frac{4}{3},-\frac{23}{22})$
3. $(-\frac{5}{3},-\frac{23}{22})$
4. None of these

Q. Find the value of $2^{3-{\log }_{2}3}$

Q. If $2+\log x=\log 45-\log 2+\log 16-2\log 3$ and $x$ = $\frac{m}{10}$, then the value of $m$ is equal to

1. $5$
2. $8$
3. $2$
4. $4$

Q.

Find the value of ${\log }_2.{\log }_{3}9$

__

Q. ${\log }_{3}3+{\log }_{4}16$

Q. If ${10}^{{log}_a\left({log}_b\right({log}_{c}x\left)\right)}=1$ and ${10}^{\left({log}_b\right({log}_c\left({log}_{a}x\right)\left)\right)}=1$, then , a is equal to

1. a/b
2. $c^{a/b}$
3. ab
4. $c^{b/c}$

Q. If ${20}^{-x}=\frac{1}{7}$ then find the value of ${20}^{2x}$.

Q. How do you Solve for $x:lo{g}_5(4x-3)=2$?

Q. Which of the following values are equal to $\log 125$?

1. $100\log 1.25$
2. $5\log 3$
3. $3\log 25$
4. $3\log 5$
5. $\log 25\log 5$

Q. The value of $a^{\log \left(b/c\right)}\times b^{\log \left(c/a\right)}\times c^{\log \left(a/b\right)}$ is

1. 0
2. 1
3. -1
4. None of these

Q. For positive number of a, k, T and S where neither 'a' nor 'S' equals unity, if $\left({\log }_{s}a\right)\left(a^{{\log }_{a}k}\right)=1-\left({\log }_{S}a\right)\left({\log }_{a}T\right)$ then S equals -

1. $Tk$
2. $T{a}^k$
3. $T{a}^{-k}$
4. $T-a^k$

Q. $\log V=2\log 2-\log 3+\log \pi +3\log r$ gives $V=\frac{4}{3}\pi r^3$

1. True
2. False

Q. Find the value of ${\log }_{9}729+{\log }_{2}32$

Q. Compute the following
$\sqrt[3]{35^{\frac{1}{{\log }_{7}5}+\frac{1}{(-{\log }_{10}0.1)}}}$

Q. find the value of 3 / root 5 + root 2 + 7 / root 5 minus root 2 , if root 5 is equal to 2.2 36 and root 2 is equal to 1.414

Q. find the value of root over 245 /root over 5