Standard Logarithm

Q. The value of ${81}^{\left(1/{\log }_{5}3\right)}+{27}^{{\log }_{9}36}+3^{\left(4/{\log }_{7}9\right)}$ is

Q. The value of $3^{\sqrt{{\log }_{3}4}}$ is equal to

1. $3^{\sqrt{{\log }_{4}3}}$
2. $4^{\sqrt{{\log }_{4}3}}$
3. $4^{\sqrt{{\log }_{3}4}}$
4. $0$

Q. If $4^{{\log }_{9}x}-6x^{{\log }_{9}2}+2^{{\log }_{3}27}=0,$ then the possible value(s) of $x$ is/are

1. $2$
2. $2^9$
3. $9$
4. $81$

Q. If ${\log }_{12}27=a$, then $\frac{3-a}{3+a}=$

1. ${\log }_{6}2$
2. $1+{\log }_{3}2$
3. $1-{\log }_{3}2$
4. ${\log }_{6}3$

Q. If ${\log }_{a}b=2,{\log }_{b}c=2$ and ${\log }_{3}c=3+{\log }_{3}a,$ then the value of $a+b+c$ is

1. $102$
2. $243$
3. $90$
4. $93$

Q. If ${\log }_3(2x+6)$ is defined, then the complete set of values of $x$ is

1. $(6,\infty )$
2. $(3,\infty )$
3. $(-6,\infty )$
4. $(-3,\infty )$

Q. If ${\log }_{3}4\cdot {\log }_{4}5\cdot {\log }_{5}6\cdots {\log }_{n-1}\left(n\right)=4$, then the value of $n$ is

Q. If ${\log }_{10}(2^x+1)+2x={\log }_{10}6+x{\log }_{10}50$, then the value of $x$ is

Q. The value of the expression ${\log }_{\pi }{\pi }^7+{\log }_{1/\pi }{\pi }^3$ is

Q. The value of $(({\log }_{2}9{)}^2{)}^{\frac{1}{{\log }_2\left({\log }_{2}9\right)}}\times (\sqrt{7}{)}^{\frac{1}{{\log }_{4}7}}$ is

1. $5$
2. $6$
3. $7$
4. $8$

Q. If the minimum value of the expression $\frac{2^{{\log }_{\sqrt{2}}{x}^2}-3^{{\log }_{27}(x^2+1{)}^3}-2x}{7^{2{\log }_{49}{x}^2}-x-1}$ is $k,$ then $4k$ equals to

Q. If $x={\log }_{2\sqrt{3}}1728$, then the value of x is

1. 5
2. 6
3. 7
4. 8

Q. If ${\log }_2\left(\frac{x-1}{x-2}\right)>0$, then

1. $x<2$
2. $x>2$
3. $x<1$
4. $x>1$

Q.

Find the value of ${\log }_{e}144$.

1. $2{\log }_{e}12$

2. $4{\log }_{e}2+2{\log }_{e}3$

3. $3{\log }_{e}2+{\log }_{e}18$

4. All of these

Q.

The product of two rational numbers is always a _____.