Conditions for the Base

Q.

If log₁₀a = x, log₁₀b = y, then value ab is

1. 10^x+y

2. 100

3. xy

4. 10^x-y

Q. If $a=x^{m+n}\cdot x^l;b=x^{n+l}\cdot x^m$ and $c=x^{l+m}\cdot x^n$. Prove that: $a^{m-n}\cdot b^{n-l}\cdot c^{l-m}=1$

Q. The value of $lo{g}_{2}lo{g}_3....lo{g}_{100}^{{100}^{{99}^{{98}^{{⋮}^{2^1}}}}}$

1. 0
2. 1
3. 2
4. 100!

Q. The value of $lo{g}_{10}2+1$ in the form of $lo{g}_{10}x$ is?

1. $lo{g}_{10}30$
2. $lo{g}_{10}50$
3. $lo{g}_{10}20$
4. $lo{g}_{10}40$

Q. Find the value of $lo{g}_{3}4.lo{g}_{4}5.lo{g}_{5}6.lo{g}_{6}7.lo{g}_{7}8.lo{g}_{8}9$.

1. 2

Q.

log abc to the base ___ is 1

1. abc

2. bc

3. ca

4. ab

Q. If $3=k.2^r$ and $15=k.4^r$, then find the value $r$

1. ${\log }_{8}5$
2. ${\log }_{5}5$
3. None of these
4. ${\log }_{2}5$

Q. If $\log 2=0.3010$ and $\log 3=0.4771$, then the value of $\log 3.6$ is $0.5562$.
If true then write 1 and if false then write 0.

Q.

log 0.5 to the base 2 is ___

1. 0

2. -1

3. -3

4. -2

Q. The value of x, if ${\log }_{10}x=-2$ is $k$.

Q. ${\log }_{10}(x+1)+lo{g}_{10}(x-1)=lo{g}_{10}11+2lo{g}_{10}3$
The value of x is .

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

Q. ${\log }_{10}(x+1)+lo{g}_{10}(x-1)=lo{g}_{10}11+2lo{g}_{10}3$
Calculate the value of x.

Q. If ${\log }_{02}(x-1)>{\log }_{004}(x+5)$ then

1. $-1<x<4$
2. $1<x<3$
3. $2<x<3$
4. $1<x<4$

Q. If $A=lo{g}_{2}lo{g}_{2}lo{g}_{4}256+2lo{g}_{\sqrt{2}}2$, then A is equal to

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

Q. The values of ${\log }_{5}125+{\log }_{2}2$

1. 4
2. $\infty$
3. 1
4. 0

Q.

log 0.2 to the base ___ is -1

1. 10

2. 5

3. 2

4. 1

Q.

If $y=2^{\frac{1}{{\log }_{x}4}}$. Then

1. $y=x$

2. $y=x^{\frac{1}{2}}$

3. $y=x^3$

4. $y=x^2$

Q. ${\log }_{10}(x+1)+lo{g}_{10}(x-1)=lo{g}_{10}11+2lo{g}_{10}3$
The value of x is .

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

Q. Express $\log 36$ in terms of $\log 2$ and $\log 3$

1. $2\log 2+2\log 2$
2. $3\log 2+2\log 3$
3. $2\log 2-2\log 3$
4. $2\log 2+2\log 3$

Q. ${\log }_{5}125=3\iff 5^3=125$

1. False
2. True

Q. ${\log }_{10}5+{\log }_{10}2=1$

1. False
2. True

Q.

log 32 to the base 2 is ___

1. 5

2. 4

3. 3

4. 1

Q. The value of $(\frac{1}{lo{g}_{3}60}+\frac{1}{lo{g}_{4}60}+\frac{1}{lo{g}_{5}60})$ is

1. 0
2. 1
3. 5
4. 60

Q.

log 5 to the base 25 is

1. 2

2. 1

3. 0.5

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

Q.

log 5 to the base 625 is

1. 0

2. 0.25

3. 0.5

4. 1

Q.

log abc to the base ___ is 1

1. bc

2. ab

3. ca

4. abc

Q. Find : ${\log }_{10}100000$

1. $4$
2. $5$
3. $10$
4. $1$

Q. Find $n$, so that
$a)$ ${\left(\frac{4}{5}\right)}^3\times {\left(\frac{4}{5}\right)}^{-6}={\left(\frac{4}{5}\right)}^{2n-1}$
$b)$ $n\left(3^{-5}\right)=3$
$c)$ $n{\left(-5\right)}^4÷n^2=5$

Q. Let $x={\log }_{0.4}(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\infty )$. The value of ${\left(0.16\right)}^x$ is

1. $\frac{1}{16}$
2. $\frac{1}{4}$
3. $\frac{1}{2}$
4. $\frac{1}{8}$

Q. How do you calculate $\frac{\ln \left(4096\right)}{\ln \left(4\right)}$?