Sample QuestionsIndices and Logarithms questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
$\log (1 \times 2 \times 3)$ is equal to
- ✓
$\log 1+\log 2+\log 3$
- B
$\log 3$
- C
$\log 2$
- D
Answer: A.
View full solution →$\log \left(\frac{32}{4}\right)$ is equal to
- A
$\frac{\log 32}{\log 4}$
- ✓
$\log 32-\log 4$
- C
$2^3$
- D
Answer: B.
View full solution →$\log _2 8$ is equal to
Answer: C.
View full solution →$\log 6+\log 5$ is expressed as
- A
$\log 11$
- ✓
$\log 30$
- C
$\log \frac{5}{6}$
- D
Answer: B.
View full solution →- A
$2^0>\left(\frac{1}{2}\right)^0$
- B
$2^0<\left(\frac{1}{2}\right)^0$
- ✓
$2^0=\left(\frac{1}{2}\right)^0$
- D
Answer: C.
View full solution →Find the value of $\log 5$, if given $\log 2=0.3010$.
View full solution →Find the logarithm of 64 to the base $2 \sqrt{2}$.
View full solution →Find the value of $\log _2 \log _2 \log _2 16$.
View full solution →If $\log x+\log y=\log (x+y)$, then find the relation between $x$ and $y$.
View full solution →Simplify : $\left(x^a y^{-b}\right)^3\left(x^3 y^2\right)^{-a}$.
View full solution →Find value of $\log 0.0625$ to the base 2 .
View full solution →Find the value of $(125)^{2 / 3} \times \sqrt{25} \times \sqrt[3]{5^3} \times 5^{1 / 2}$.
View full solution →Using the world population formula $P=6.9\left(1.011^t\right.$, where $t$ is the number of years after 2011 and $P$ and 6.9 billion people in 2011 is the world population in billions of people, estimate :
(a) the population in the year 2050 to the nearest hundred million, and
(b) by what year will the population be double what it was in 2011.
View full solution →(i) Solve the following simultaneous logarithmic equations:
$\log _2\left(x y^2\right)=0, \log _2\left(x^2 y\right)=3$
(ii) Solve the following equation for $x$ :
$2 \times 3^{1 / 2 x+2}=23.43$
View full solution →(i) It is given that $x$ satisfies the logarithm equation $\log _a x=2\left[\log _a k-\log _a 2\right]$,where $k>0, a>0, a \neq 1$.
(a) Find $x$ in terms of $k$, giving the answer in the form not involving logarithm.
Suppose instead that $x$ satisfies
$\log _x(5 y+1)=4+\log _x 3$
where, $x>0, x \neq 1$, and $y>0, y \neq 1$.
(b) Solve the above equation expressing $y$ in terms of $x$, giving the answer in a form not involving logarithm.
(ii) Solve the equation $\frac{1}{6}=\left(\frac{1}{2}\right)^x$ and give your answer as single logarithm of base 2 .
View full solution →(i) If $\log _a b c=x, \log _b c a=y, \log _c a b=z$, prove that
$\frac{1}{x+1}+\frac{1}{y+1}+\frac{1}{z+1}=1$
(ii) Given that, $p=\log _a 4$ and $q=\log _a 5$Express each of the following logarithms in terms of $p$ and $q$.
(a) $\log _a 100$
(b) $\log _a 0.4$
View full solution →(i) Find the value of
$
\left(\frac{x^b}{x^c}\right)^{(b+c-a)} \cdot\left(\frac{x^c}{x^a}\right)^{(c+a-b)} \cdot\left(\frac{x^a}{x^b}\right)^{(a+b-c)}
$
(ii) If $m$ and $n$ are whole numbers such that $m^n=121$, then find the value of $(m-1)^{n+1}$.
(iii) Simplify : $\frac{(243)^{n / 5} \times 3^{2 n+1}}{9^n \times 3^{n-1}}$.
View full solution →$\log \left(\frac{1}{81}\right)$ to the base 9 is equal to _________________
View full solution →Given, $\log 2=0.3010$ and $\log 3=0.4771$, the value of $\log 6$ is _________________
View full solution →$\log _{\sqrt{2}} 64$ is equal to _________________
View full solution →The value of $\log 0.0001$ to the base 0.1 is _________________
View full solution →$\frac{\left(81 x^4\right)^{\frac{1}{4}}}{y^{-8}}$ is equal to _________________
View full solution →Simplify : $\left[1-\left\{1-\left(1-x^2\right)^{-1}\right\}^{-1}\right]^{-1 / 2}$
View full solution →Suppose that certain amount $P$ is invested at an annual rate of $6.5 \%$, compounded annually. How long will it take for the amount to triple?
[use, $\log _e 3=1.0986$ ]
View full solution →Oskie-946 has a decay rate of $13.5 \%$. If the original sample was 50 gms , how long will it take for only 10 gms of the sample to remain ?
[Given, $\log _e 0.2=-1.60943$ ]
View full solution →If $a=\log _{24} 12, b=\log _{36} 24$ and $c=\log _{48} 36$, then prove that $1+a b c=2 b c$.
View full solution →Prove that : $\frac{\log _3 8}{\log _9 16 \cdot \log _4 10}=3 \log _{10} 2$
View full solution →| Column-I | Column-II |
| (a) $\log _{10} 1000000$ | (i) 0 |
| (b) $\log _e 1$ | (ii) 6 |
| (c) $\log _{32}\left(\frac{1}{4}\right)$ | (iii) 10 |
| (d) $\log _2 1024$ | (iv) $-\frac{2}{5}$ |
| Column-I | Column-II |
| (a) The value of $2 \times(32)^{1 / 5}$ is | (i) 1 |
| (b) The value of $\frac{4}{(32)^{1 / 5}}$ is | (ii) 2/3 |
| (c) The value of $\left(\frac{8}{27}\right)^{1 / 3}$ is | (iii) 2 |
| d) The value of $2(256)^{-1 / 8}$ is | (iv) 4 |