B Nirmala Shastry Solutions for Exercise 3: MISCELLANEOUS EXERCISE

Find the value of $x$:
${\log }_5\left(x^2+9\right)=2$

Find the value of $x$:
${\log }_{x}8=2-{\log }_{x}18$

Find the value of ${\log }_{10}0.001$.

Find the value of ${\log }_{a}a$.

Express as a single logarithm:

$\frac{1}{3}\log 125-2\log 3+\frac{1}{4}\log 625$

Solve for $x$: $\log \left(4x+3\right)+\log \left(4x-3\right)=4 \log 2$

Solve for $x$: $2 \log x+\frac{1}{3}\log 125x^3=3 \log 2+\log 5$

Express $V$ in terms of other quantities in the following: $\log V+\log 3=\log \mathrm{\pi }+2 \log \mathrm{r}+\log \mathrm{h}$