Conversion of Numbers Using Logarithms

Q.

In a certain code $256$ means you are good; $637$ means we are bad and $358$ means good and bad’. What represents and in that code?

Q. $5^4=625$ can be written in logarithmic form as .

1. $lo{g}_{4}5=625$
2. $lo{g}_{5}625=4$
3. $lo{g}_{4}625=5$

Q.

If $lo{g}_2(x+y)=lo{g}_3(x-y)=\frac{log25}{log0.2}$, find the values of $x$ and $y$.

Q.

Find x, if:

(i) $lo{g}_{3}x=0$

(ii) $lo{g}_{x}2=-1$

(iii) $lo{g}_{9}243=x$

(iv) $lo{g}_5(x-7)=1$

(v) $lo{g}_{4}32=x-7$

(vi) $lo{g}_7(2x^2-1)=2$

Q.

Express each of the following in exponential form :

(i) $lo{g}_{8}0.125=-1$

(ii) $lo{g}_{10}0.01=-2$

(iii) $lo{g}_{a}A=x$

(iv) $lo{g}_{10}1=0$

Q.

$\frac{log2197}{log13}$ = _______ .

___

Q.

Evaluate:

(i) $lo{g}_{10}0.01$

(ii) $lo{g}_2(1÷8)$

Q. $5^4=625$ can be written in logarithmic form as .

1. $lo{g}_{4}5=625$
2. $lo{g}_{5}625=4$
3. $lo{g}_{4}625=5$

Q. If $log\frac{x}{y}+log\frac{y}{x}=log(x+y)$, find the value of $x+y$.

1. 1

Q. Match the following expressions with their values.

1. 3
2. $\log \left(\frac{x^2}{y^3}\right)$
3. \N
4. 1

Q. If ${\log }_2(4^{x+1}+4){\log }_2(4^x+1)={\log }_2\left(8\right)$, then $x$ is equal to

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

Q.

Solve for $x:lo{g}_{10}x=-2$

Q. Find the value of log 4 + log 5 - log 2.

1. 8
2. 2
3. 4
4. 1

Q.

If $x={\log }_{b}a$, $y={\log }_{c}b$, $z={\log }_{a}c$, then $xyz$ is

1. $0$

2. $1$

3. $2$

4. $4$

Q.

If $lo{g}_{27}x=2\frac{2}{3}$, find $x$.

Q. ${\log }_{10}5+{\log }_{10}8-2{\log }_{10}2$ =

1. ${\log }_{10}2$
2. 4
3. 1

Q. If $2^5=32$, then in logarithmic form, it can be written as

1. 5
2. 2
3. 32

Q. If the value of $\left({\log }_{10}2\right)+1$ is in the form of ${\log }_{10}m$, then $m$ is equal to

1. $11$
2. $14$
3. $20$
4. $17$

Q.

If $lo{g}_{10}a=b$, find ${10}^{3b-2}$ in terms of a.

Q. If $log$ $27$ = 1.431, find the value of:

(i) $log$ $9$

(ii) $log$ $300$

Q. ${\log }_{10}5+{\log }_{10}8-2{\log }_{10}2$ =

1. 4
2. ${\log }_{10}2$
3. 1

Q. solve $x^x=x$

Q.

Find the value of ($3^2$ + $4^{-1}$) $\times$ $2^2$

1. 37

2. 42

3. 5

4. 25

Q. Solve : $\int \frac{e^x}{x}(1+x\log x)dx$

Q. ${\log }_{b}a=\frac{{\log }_{x}a}{{\log }_{x}b}$ where x can be any real number.

1. True
2. False

Q. Solve: ${\log }_4{\log }_2{\log }_{\sqrt{2}}{\log }_3(x-2006)=0$

Q. The value of $lo{g}_{3}9+lo{g}_{5}25+lo{g}_{2}8$ is

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

Q. Express the each of following in exponential form:
${\log }_{8}0.125=-1$

Q. Which of the following statements is true?

1. log 0 = 1
2. log 100 = 1
3. log 10 = 2
4. log 1 = 0

Q.

The value of $4\log \frac{24}{25}-16\log \frac{9}{10}+7\log \frac{81}{80}$

1. $\log 9$

2. $\log 7$

3. $\log 5$

4. $\log 3$