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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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