Property 3

Q.

1. 2 log 5 + log a − log b

2. 2 log 5 − log a − log b

3. 2 log 5 + log a + log b

4. 2 log 5 − log a + log b

Q.

If $\log 2=0.3010$ and $\log 3=0.4771$ find the value of $\log 25$?

Q.

What is $\log 5$? How can we find logs of numbers without using a calculator?

Q.

If log_x5=a and log₂₀x=b then find the value of log_x10.

Q.

Find 'x' if:

log (x-1) + log (x+1) = log_​2​​​1.

Q.

log(x-y)=logx-logy

1. True

2. False

Q.

If logm+logn=log(m+n) find the value of m in terms of n

Q.

Given $x=lo{g}_{10}12$, $y=lo{g}_{4}2\times lo{g}_{10}9$ and $z=lo{g}_{10}0.4$, find :

(i) $x-y-z$

(ii) ${13}^{x-y-z}$

Q.

The value of $1-\log 2+\frac{(\log 2{)}^2}{2!}-\frac{(\log 2{)}^3}{3!}+...$ is

1. $\log 3$

2. $\log 2$

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

4. None of these

Q.

If $a^2=logx$, $b^3=logy$ and $\frac{a^2}{2}-\frac{b^3}{3}=logc$, find c in terms of $x$ and $y$.

Q.

The value of $a={\log }_2\left({\log }_2\left({\log }_4\left(256\right)\right)\right)+2{\log }_{\sqrt{2}}\left(2\right)$ then $a$ is

1. $1$

2. $2$

3. $3$

4. $4$

5. $5$

Q. Simplify the following and express with positive index:
${\left(\frac{(27{)}^{-3}}{9^{-3}}\right)}^{\frac{1}{5}}$

Q.

If ${\log }_x\left(ax\right),{\log }_x\left(bx\right)$ and ${\log }_x\left(cx\right)$ are in AP, where $a,b,c$ and $x$ belong to $(1,\infty )$, then $a,b$ and $c$ are in

1. A.P.

2. H.P.

3. G.P.

4. None of these

Q.

The value of ${\log }_3\left(4\right){\log }_4\left(5\right){\log }_5\left(6\right){\log }_6\left(7\right){\log }_7\left(8\right){\log }_8\left(9\right)$ is

1. $1$

2. $2$

3. $3$

4. $4$

Q.

Simplify: $\left|-21\right|+\left|-31\right|÷2$

Q.

Given $2lo{g}_{10}x+1=lo{g}_{10}250$, find :

(i) $x$

(ii) $lo{g}_{10}2x$

Q.

Solve:

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

Q.

Question 4(i)
Shade
$\frac{1}{2}$ of the circles in box

Q.

If $\frac{loga}{b-c}=\frac{logb}{c-a}=\frac{logc}{a-b}$, then $a^a.b^b.c^c=$

1. 2

2. -1

3. None of the above

4. 1

Q.

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

1. 4 log_e 2+2 log_e 3

2. log_e 2 + log_e 18

3. 2 log_e 12

4. All of these

Q.

If $m=log20$ and $n=log25$, find the value of x, so that : $2log(x-4)=2m-n$.

Q.

(i) If $log(a+1)=log(4a-3)-log3$; find a.

(ii) If $2logy-logx-3=0$, express x in terms of y.

(iii) Prove that : $lo{g}_{10}125=3(1-lo{g}_{10}2)$.

Q.

If $p=log20$ and $q=log25$, find the value of $x$, if $2log(x+1)=2p-q$.

Q.

If $f\left(x\right)={\log }_x\left(\log x\right)$, then $f\left(x\right)$ at $x=e$ is

1. $e$

2. $\frac{1}{e}$

3. $1$

4. None of these.

Q. Is log N to the base a always unique? explain

Q. Find x, if
\(4^{2x}=\dfrac{1}{32}\)

Q. express $\log q^3-\log 64+\frac{1}{2}\log 16$ as a single logarithm.

Q. If $\frac{logx}{y-z}=\frac{logy}{z-x}=\frac{logz}{x-y}$ , then $xyz=?$

Q. If p(x) = x = 4, then p(x) + p(−x) = ?
(a) 0
(b) 4
(c) 2x
(d) 8

Q.

If $x=log0.6;y=log1.25$ and $z=log3-2log2$, find the values of :

(i) $x+y-z$

(ii) $5^{x+y-z}$