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Mathematics
Properties of logarithm
How do you solve ${3^{2 - x}} = {5^{2x + 1}}$?

Mathematics
Properties of logarithm
If ${\log _{12}}27 = a$, then what is ${\log _6}16$ ?
Mathematics
Properties of logarithm
Is $\left({ln\ x} \right)^{2}$ equivalent to $ln^{2}\left( x \right)$ ?

Mathematics
Properties of logarithm
How do you evaluate ${\log _2}1$ ?

Mathematics
Properties of logarithm
How do you evaluate ${\log _{16}}1?$
Mathematics
Properties of logarithm
How do you find the value of ${\log _{\dfrac{1}{2}}}15$ using the change of base formula?
Mathematics
Properties of logarithm
How do you write ${\log _3}243 = 5$ in exponential form.

Mathematics
Properties of logarithm
If x, y, z are three consecutive positive integers, then ${\log _e}\sqrt x + {\log _e}\sqrt z + \dfrac{1}{{2xz + 1}} + \dfrac{1}{3}{\left( {\dfrac{1}{{2xz + 1}}} \right)^3} + \dfrac{1}{5}{\left( {\dfrac{1}{{2xz + 1}}} \right)^5} + ...$ is
A.${\log _e}\sqrt y$
B.${\log _e}y$
C.${\log _e}{y^2}$
D.None of these

Mathematics
Properties of logarithm
Solve for x:
${{\log }_{\dfrac{3}{4}}}{{\log }_{8}}({{x}^{2}}+7)+{{\log }_{\dfrac{1}{2}}}{{\log }_{\dfrac{1}{4}}}{{({{x}^{2}}+7)}^{-1}}=-2$
This question has a multiple correct option
A). $x=3$
B). $x=5$
C). $x=-3$
D). $x=6$

Mathematics
Properties of logarithm
We have an equation ${\log _2}^{\left( {9 - {2^x}} \right)} = {10^{{{\log }^{(3 - x)}}}}$. Solve for $x$.
a). 0
b). 3
c). Both (a) and (b)
d). 0 and 6
Mathematics
Properties of logarithm
Express each of the following as a single logarithm:
$\dfrac{1}{2}\log 36 + 2\log 8 - \log 1.5$

Mathematics
Properties of logarithm
If $x$ , $y$ , $z$ are in HP, then $\log \left( {x + z} \right) + \log \left( {x - 2y + z} \right)$ is equal to
$1){\text{ }}\log \left( {x - z} \right)$
$2){\text{ 2}}\log \left( {x - z} \right)$
$3){\text{ 3}}\log \left( {x - z} \right)$
$4){\text{ 4}}\log \left( {x - z} \right)$

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