M L Aggarwal Solutions for Exercise 2: EXERCISE 9.2

If $a= \log \frac{2}{3}, b=\log \frac{3}{5}$and $c= 2 \log \sqrt{\frac{5}{2}}$ find the value of: $5^{a+b+c}$

If $x=\log \frac{3}{5},\hspace{0.17em}y=\log \frac{5}{4} and z=2\log \frac{\sqrt{3}}{2}$, find the values of

$x+y-z.$

If $x=\log \frac{3}{5},\hspace{0.17em}y=\log \frac{5}{4} and z=2\log \frac{\sqrt{3}}{2}$, find the value of $3^{ x+y-z.}$

If $x=lo{g}_{10}12,\hspace{0.17em}y=lo{g}_{4}2\times lo{g}_{10}9$ and $z=lo{g}_{10}0.4,$ find the value of $7^{ x-y-z}$

Given $3(\log 5 – \log 3) – (\log 5 – 2 \log 6) = 2 – \log n$, find $n$.

Solve the given equations :

Show that :$\frac{1}{{\log }_{8}36}+\frac{1}{{\log }_{9}36}+\frac{1}{{\log }_{18}36}=2$ 

Prove the following identities :

$\frac{1}{{\log }_{a}abc}+\frac{1}{{\log }_{b}abc}+\frac{1}{{\log }_{c}abc}=1$