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Mathematics
Exponents and logarithms
What is $\ln ({i^2})$?
Mathematics
Exponents and logarithms
How do you simplify $\ln \left( {\ln {e^{{e^{10}}}}} \right)$?
Mathematics
Exponents and logarithms
How do you evaluate $\log 0.003$?

Mathematics
Exponents and logarithms
What is the value of the expression ${\left( { - 3} \right)^4}$ ?
Mathematics
Exponents and logarithms
If $\log 4 + 2\log 3$ is $\log m$ ,then the value of $m$ is equal to
(a) $33$
(b) $31$
(c) $36$
(d) $38$

Mathematics
Exponents and logarithms
Given that $a,b\in \left\{ 0,1,2,.....9 \right\}$ with $a+b\ne 0$ and ${{\left( a+\dfrac{b}{10} \right)}^{x}}={{\left( \dfrac{a}{10}+\dfrac{b}{100} \right)}^{y}}=1000$ .Then $\left( \dfrac{1}{x} \right)-\left( \dfrac{1}{y} \right)=$
1) $1$
2) $\dfrac{1}{2}$
3) $\dfrac{1}{3}$
4) $\dfrac{1}{4}$
Mathematics
Exponents and logarithms
If the equation ${2^x} + {4^y} = {2^y} + {4^x}$ is solved for y in terms of x, where $x < 0$ , then the sum of the solution will be:
$1.\,\,x{\log _2}\left( {1 - {2^x}} \right)$
$2.\,\,x + {\log _2}\left( {1 - {2^x}} \right)$
$3.\,\,{\log _2}\left( {1 - {2^x}} \right)$
$4.\,\,x{\log _2}\left( {{2^x} + 1} \right)$

Mathematics
Exponents and logarithms
If ${\log _a}x,{\log _b}x,{\log _c}x$ are in A.P. where $x \ne 1$ then show that ${c^2} = {(ac)^{{{\log }_a}b}}$.

Mathematics
Exponents and logarithms
Solve: ${{\left( 100 \right)}_{2}}-{{\left( 10 \right)}_{2}}$
$\left( A \right)\text{ }{{\left( 11 \right)}_{2}}$
$\left( B \right)\text{ }{{\left( 01 \right)}_{2}}$
$\left( C \right)\text{ }{{\left( 10 \right)}_{2}}$
$\left( D \right)\text{ }{{\left( 101 \right)}_{2}}$
Mathematics
Exponents and logarithms
The number of digits in ${20^{301}}$ ( given , ${\log _{10}}2 = 0.3010$) is
A.$602$
B.$301$
C.$392$
D.$391$

Mathematics
Exponents and logarithms
If $y={{2}^{\dfrac{1}{{{\log }_{x}}4}}}$ , then $x$ is equal to
A. $y$
B. ${{y}^{2}}$
C. ${{y}^{3}}$
D. none of these

Mathematics
Exponents and logarithms
What is  $\dfrac{1}{{{{\log }_2}N}} + \dfrac{1}{{{{\log }_3}N}} + \dfrac{1}{{{{\log }_4}N}}... + \dfrac{1}{{{{\log }_{100}}N}}$ equal to $(N \ne 1)$ ?

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