Basics of Logarithm

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

The natural logarithm of a number is represented as $\log$ with base $10$.

The natural logarithm of $8$ is ${\log }_{10}8$ .

Find the natural logarithm of $3$.

${10}^{ {\log }_p\left({\log }_q\left({\log }_{r}x\right)\right)}=1$ and ${\log }_q\left({\log }_r\left({\log }_{p}x\right)\right)=0$, then $p$ equals to

If ${\log }_{125}5x = {\log }_{343}7x,$ then the value of ${\log }_{42}(x^4-2x^2+7)$ is :

Given: $B\left(n\right)=16\left({\sin }^n\theta +{\cos }^n\theta \right)$. If $m$ is the minimum value of $\frac{B\left(6\right)}{16}$, then the characteristic of ${\log }_{10}\left(m\right)$, is equal to: $\left({\log }_{10}2=0.301\right)$

The number of zeros coming immediately after the decimal point in the value of ${\left(0.2\right)}^{25}$ is/are (given ${\log }_{10}2 = 0.30103$ )

${\log }_{4}18$ is-

Logarithm of $32\sqrt[5]{4}$ to the base $\left(2\sqrt{2}\right)$ 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 :${\left(\sqrt{2}\right)}^6=8$.