Basics of Logarithm

Solve the equation, ${\log }_3{\left(\frac{x-3}{x-7}\right)}^2+1={\log }_3\left(\frac{x-3}{x-1}\right)$

If ${\log }_{10}2=a \mathrm{and} {\log }_{2}3=b$, then express ${\log }_{4}100-2{\log }_{27}100$ in terms of $a$ and $b$.

Solve, $3^x=2^{x+1}$.

Find $\frac{\left(17.56\times 3^7\right)}{\left(4.75\times 2^4\right)}$ using logarithm table.  [Use $\log \left(17.56\right)=1.2445;\log 3=0.4771;\log \left(4.75\right)=0.6767;\log 2=0.3010$]

Find the value with the help of logarithm tables:

$5872\times 0.058$.  [Use $\log 58.72=1.77;\log 58=1.76$]

The value of the logarithm ${\log }_{2}1/4$ is

If ${\log }_4{\log }_3{\log }_{2}x=0$, then $x$ is equal to

Find the value of ${\log }_9\left(\frac{1}{3}\right)$.

Find the value of ${\log }_2\left(\frac{1}{32}\right)$.

Find the value of ${\log }_{10}1000$.

Find the value of ${\log }_{3}243$.

Find the value of ${\log }_{4}256$.

Find the value of $x$ from the equation ${\log }_2 (0.5)=x$

Find the value of ${\log }_{10}10$.

Write in logarithmic form :$2^{-6}=\frac{1}{64}$.

Write in logarithmic form :${\left(\sqrt{2}\right)}^6=8$.

Write in logarithmic form :${10}^{-2}=0.01$.

Write in logarithmic form :${10}^4=10000$.

Write in logarithmic form : $3^{-3}=\frac{1}{27}$

Write in logarithmic form :$2^4=16$.