Property 1

Q.

How do you calculate $\log \left(0.1\right)$?

Q.

The value of $\frac{\left({\log }_3\left(5\right)\times {\log }_{25}\left(27\right)\times {\log }_{49}\left(7\right)\right)}{{\log }_{81}\left(3\right)}$ is

1. $1$

2. $6$

3. $\frac{2}{3}$

4. $3$

Q.

If $lo{g}_{6}216=x$, what is the value of x?

___

Q.

Express each of the following as a single logarithm: $\frac{1}{2}\log \left(36\right)+2\log \left(8\right)-\log \left(1.5\right)$.

Q.

$\text{Solve for}x\text{in the equation}$ $log\left[log\right(2+lo{g}_2(x+1)\left)\right]=0$

1. $2^8-1$

2. $2^8$

3. $2^2-1$

4. $3^8-1$

Q.

Prove that $\sqrt{\frac{1}{4}}+(0.01{)}^{-\frac{1}{2}}-(27{)}^{\frac{2}{3}}=\frac{3}{2}$

Q.

The sum of the series ${\log }_9\left(3\right)+{\log }_{27}\left(3\right)-{\log }_{81}\left(3\right)+{\log }_{243}\left(3\right)-...$ is

1. $1-{\log }_e\left(2\right)$

2. $1+{\log }_e\left(2\right)$

3. ${\log }_e\left(2\right)$

4. $1+{\log }_e\left(3\right)$

Q. Simplify the following and express with positive index:
$(32{)}^{-\frac{2}{5}}÷(125{)}^{-\frac{2}{3}}$

Q. If $2^x=3^y={12}^z$, prove that $-\frac{2}{x}+\frac{1}{y}+\frac{1}{z}=0$

Q.

Factor out the coefficient of the variable term.

$\frac{3}{8}z+1$

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

1. $\log 3$
2. $\log 6$
3. $\log 2$
4. $\log 5$

Q.

If ${\log }_{10}2=0.3010$, the value of ${\log }_{10}80$ is

1. $1.6020$

2. $1.9030$

3. $3.9030$

4. None of these

Q. If $7^x=1000$ then, x=_____.

1. $\frac{3}{log7}$
2. $\frac{9}{3log7}$
3. $\frac{7}{log3}$
4. $\frac{3}{7}$

Q.

1. $0.69005$
2. $0.6905$
3. $1.695$
4. $1.3801$

Q. Show that : $7\log \left(\frac{16}{15}\right)+5\log \left(\frac{25}{24}\right)+3\log \left(\frac{81}{80}\right)=\log 2$.

Q. Evaluate: $2{\tan }^{2}45+{\cos }^2{30}^{\circ }-{\sin }^2{60}^{\circ }$

1. $2$
2. $4$
3. $6$
4. $3$

Q.

How do you evaluate $\log 1$?

Q. Integrate the following function: $\frac{e^{2x}-e^{-2x}}{e^{2x}+e^{-2x}}$

Q. If $a^2+b^2=7ab$ then show that $\log \left(\frac{a+b}{3}\right)=\frac{1}{2}\log a+\frac{1}{2}\log b$

Q. Solve the following equations.
$log(3+2log(1+x\left)\right)=0.$

Q.

_____ hectares = 1 km²

Q. If log2x=0 , then x =

1. 1
2. -1
3. 0

Q. $2\log 2-3\log 4$ can be written as a single logarithm with base as $10$ as______

1. $\log \frac{8}{81}$
2. $\log 12$
3. $\log 81$
4. $\log \frac{4}{64}$

Q.

If $b$ is any number such that $b>0$ and $b\ne 1$ then, $lo{g}_{b}1$=___

Q.

log 3430 = ________________ .

1. 3 log 7 + log 10

2. 2 log 7 + log 10

3. log 7 + 2 log 10

4. log 7 + log 10

Q. Solve:

Q.

Calculate the value of the following :

${\left(\frac{12}{11}\right)}^3$

Q. If $lo{g}_{10}2=0.3010$, the value of $lo{g}_{10}$ 80 is

1. 1.602
2. 1.903
3. 3.903
4. None of these

Q. Solve:

Q. Solve for $x$ the following equation:
$lo{g}_{(2x+3)}(6x^2+23x+21)=4-lo{g}_{(3x+7)}(4x^2+12x+9)$.

1. $-2$
2. $-\frac{1}{4}$
3. $-4$
4. $none$