Property 4

Q.

What is the value of $\log 7$ base $2$.

Q.

Simplify $3x\left(4x-5\right)+3$ and find its values for

(i) $x=3$

(ii)$x=\frac{1}{2}$

Q.

Simplify: $\log \left(\frac{70}{33}\right)+\log \left(\frac{22}{135}\right)-\log \left(\frac{7}{18}\right)$

Q.

If $lo{g}_{30}3=c,lo{g}_{30}5$ then the value of $lo{g}_{30}8$

1. 2(1-c-d)
   

2. 3(1+c-d)
   

3. 3(1+c+d)
   

4. 3(1-c-d)

Q.

The antilog of $\frac{5}{6}$ to the base $64$ is

Q.

Given : $\frac{logx}{logy}=\frac{3}{2}$ and $log\left(xy\right)=5$; find the values of $x$ and $y$.

Q.

If $x\ne 0$and $y={\log }_e\left|2x\right|$, then $\frac{dy}{dx}$ is equal to

1. $\frac{1}{x}$

2. $\frac{-1}{x}$

3. $\pm \frac{1}{2x}$

4. None of these

Q.

If ${\left(150\right)}^{\mathrm{x}}=7$, then $\mathrm{x}$ is equal to :

Q.

Given: $lo{g}_{3}m=x$ and $lo{g}_{3}n=y$.

(i) Express $3^{2x-3}$ in terms of m.

(ii) Write down $3^{1-2y+3x}$ in terms of m and n.

(iii) If $2lo{g}_{3}A=5x-3y$; find A in terms of m and n.

Q.

Express each of the following in a form free from logarithm:

(i) $2logx-logy=1$

(ii) $2logx+3logy=loga$

(iii) $alogx-blogy=2log3$

Q.

Find x, if :

$x-log48+3log2=\frac{1}{3}log125-log3$

Q. 25 Kanwar is three years older than anima Six years ago kanwars age was three times animas age find the ages of kanwar and anima

Q. Evaluate : $2^{{\log }_{3}5}-5^{{\log }_{3}2}$

Q. If $a=lo{g}_{24}12,b=lo{g}_{36}24,c=lo{g}_{48}36$, then $1+abc$ is equal to

1. $2ac$
2. $2bc$
3. $2ab$
4. None of these

Q. If (a^2)+(b^2)+(1)/(a^2)+(1)/(b^2)=4 then the value of (a^2+b^2)^1/2=?

Q. 14. If a+b=10 then value of a2 + b2 -10a-10b + 2ab + 5is

Q. If $\frac{\mathrm{logx}}{b-c}=\frac{\log y}{c-a}=\frac{\log z}{a-b},$ then show that $x^{b+c}.y^{a+b}.z^{a+b}=1$

Q. The value of ${\log }_{15}{225}^{225}$ is equal to

1. $15$
2. $375$
3. $225$
4. $450$

Q. If $a=lo{g}_{24}12,b=lo{g}_{36}24,c=lo{g}_{48}36$, then $1+abc$ is equal to

1. None of these
2. $2ac$
3. $2bc$
4. $2ab$

Q.

Cofunction of cot20 is

1. tan20

2. cos20

3. tan70

4. tan25

Q. If $lo{g}_{10}2,lo{g}_{10}(2^x-1)$ and $lo{g}_{10}(2^x+3)$ be three consecutive terms of an A.P., then proove $x=lo{g}_{2}5$.

Q.

If $lo{g}_{12}27=a$, then $lo{g}_{6}16=$

1. None of these

2. $2\frac{3-a}{3+a}$

3. $3\frac{3-a}{3+a}$

4. $4\frac{3-a}{3+a}$

Q.

$\frac{1}{lo{g}_{xy}xyz}+\frac{1}{lo{g}_{yz}xyz}+\frac{1}{lo{g}_{zx}xyz}=$

1. 0

2. 1

3. 2

4. $lo{g}_{zx}xyz$

Q. If $\log 625=k\log 5$, then the value of $k$ is ____

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

Q. Find the zeroes of the polynomial $p\left(x\right)=x-{\log }_{2}16$.

Q. The value of x satisfying the equation $4^{{{\log }_9}^3}+9^{{{\log }_2}^4}={10}^{{{\log }_c}^{83}}$ is

Q. Solve the following equations.
${6.9}^{0.5x-2}+{2.3}^{x-6}=56.$

Q. The value of ${10}^{{\log }_{10}{10}^7}$ is:

1. $7$
2. ${10}^7$
3. $10$
4. ${\log }_{10}7$

Q. If $\log (x+4)-\log (x-4)=\log 2$, then the value of $x$ is equal to

1. $4$
2. $-2$
3. $-5$
4. $12$

Q. Find $x$ if
a) $2^x=22$
b) $3^x=243$