## Sequence and Series Questions and Answers Part-17

1. if $a^{2}+4b^{2}=12ab$     then $\log\left(a+2b\right)=$
a) $\frac{1}{2}\log\left(\frac{ab}{2}\right)$
b) $\frac{1}{2}\log a+\frac{1}{2}\log b+2\log 2$
c) $\frac{1}{2}\log\left(\frac{16a}{2}\right)$
d) $\frac{1}{2}\left(\log\frac{ab}{16}\right)$

Explanation:

2. The solutions set the inequality $\log_{10}\left(x^{2}-16\right)\leq\log_{10}\left(4x-11\right)$
is
a) $\left(4,\infty\right)$
b) $\left(4,5\right]$
c) $\left(11/4,\infty\right)$
d) $\left(11/4,5\right)$

Explanation:

3. If $\log_{12}18=\alpha$    and $\log_{24}54=\beta$    then the value of $\alpha\beta+\left(\alpha-\beta\right)$   is
a) 2
b) $\log_{12}24$
c) 1
d) none of these

Explanation:

4. The solutions set of $\log_{11}\log_{7}\left(\sqrt{x+5}+\sqrt{x}\right)=0$       is
a) {7}
b) {11}
c) {441/25}
d) none of these

Explanation:

5. If $\log_{x}2+\log_{x^{2}}\left(2\right)>1$      , then x lies
a) $\left(1,2\sqrt{2}\right)$
b) $\left(2\sqrt{2},\infty\right)$
c) $\left(2,\infty\right)-\left\{2\sqrt{2}\right\}$
d) $\left(2\sqrt{2},5\right)$

Explanation:

6. If x satisfies $\log_{2}\left(9^{x-1}+7\right)=2+\log_{2}\left(3^{x-1}+1\right)$
then
a) $x\epsilon Q$
b) $x\epsilon \left\{x\epsilon Q:x<0\right\}$
c) $x\epsilon N$
d) Both a and c

Explanation:

7. If $\frac{\log x}{b-c}=\frac{\log y}{c-a}=\frac{\log z}{a-b}$      then which of the folloe=wing are true
a) xyz=1
b) $x^{a}y^{b}z^{c}=1$
c) $x^{b+c}y^{c+a}z^{a+b}=1$
d) All of the Above

Explanation:

8. If $x^{\left(\log_{2}x\right)^{2}-6\log_{2}x+11}=64$       then x is equal to
a) 2
b) 4
c) 8
d) All of the Above

Explanation:

9. If a,b,c are consecuritive positive integers and $\log\left(1+ac\right)=2k$     then the value of k is
a) $\log b$
b) $\log a$
c) 2
d) Both a and b

10. If $\log_{a}bc=x,\log_{b}ca=y,\log_{c}ab=z$         then the value of $\frac{1}{x+1}+\frac{1}{y+1}+\frac{1}{z+1}$