What is $\ln$ in logarithm$?$

Important Questions on Functions

MEDIUM

Mathematics>Differential Calculus>Functions>Special Functions

If $3^{x+1}=6^{{\log }_{2}3}$, then $x$ is:

MEDIUM

Mathematics>Differential Calculus>Functions>Special Functions

The value of ${\left({\left({\log }_{2}9\right)}^2\right)}^{\frac{1}{{\log }_2\left({\log }_{2}9\right)}}\times {\left(\sqrt{7}\right)}^{\frac{1}{{\log }_{4}7}}$ is

MEDIUM

Mathematics>Differential Calculus>Functions>Special Functions

If  ${\log }_{\sqrt{3}} x+{\log }_{\sqrt[3]{5}} x+{\log }_{\sqrt[4]{5}} x+......$  up to $7$ terms $=35$, then the value of $x$ is :

EASY

Mathematics>Differential Calculus>Functions>Special Functions

If $2^x{.3}^{x+4}=7^x$, then $x$ is equal to

EASY

Mathematics>Differential Calculus>Functions>Special Functions

For which of the following values of $\text{'}x\text{'},$ does the function $f\left(x\right)=\log \left[\left\{\sqrt{\left(25-x^2\right)}\right\}/\left(2-x\right)\right]$have the real values?

MEDIUM

Mathematics>Differential Calculus>Functions>Special Functions

If ${\log }_{2}6+\frac{1}{2x}={\log }_2\left(2^{\frac{1}{x}}+8\right)$ then the values of $x$ are

EASY

Mathematics>Differential Calculus>Functions>Special Functions

The logarithm of $\frac{1}{256}$ to the base $2\sqrt{2}$ is

MEDIUM

Mathematics>Differential Calculus>Functions>Special Functions

The value of ${\log }_{2}32=$

MEDIUM

Mathematics>Differential Calculus>Functions>Special Functions

Let $a, b, c$ be the three distinct positive real numbers such that ${\left(2a\right)}^{{\log }_{e}a}={\left(bc\right)}^{{\log }_{e}b}$ and $b^{{\log }_{e}2}=a^{{\log }_{e}c}$ Then $6a+5bc$ is equal to ______.

MEDIUM

Mathematics>Differential Calculus>Functions>Special Functions

The number of integral solution $x$ of ${\log }_{\left(x+\frac{7}{2}\right)}{\left(\frac{x-7}{2x-3}\right)}^2\ge 0$ is

MEDIUM

Mathematics>Differential Calculus>Functions>Special Functions

${\log }_7{\log }_7\sqrt{7\sqrt{7\sqrt{7}}}$ is equal to

EASY

Mathematics>Differential Calculus>Functions>Special Functions

$\sum _{n=1}^{\infty }\frac{2n^2+7n+5}{n!}$ is equal to

HARD

Mathematics>Differential Calculus>Functions>Special Functions

If $N=m!$ (where $m$ is a fixed positive integer $>2$), then $\frac{1}{{\log }_{2}N}+\frac{1}{{\log }_{3}N}+\frac{1}{{\log }_{4}N}+\mathrm{.....}+\frac{1}{{\log }_{m}N}=$

EASY

Mathematics>Differential Calculus>Functions>Special Functions

If $a={\log }_{2}3,b={\log }_{2}5$ and $c={\log }_{7}2$, then ${\log }_{140}63$ in terms of $a,b,c$ is

EASY

Mathematics>Differential Calculus>Functions>Special Functions

If $a^x=b^y=c^z=d^w$, the value of $x\left(\frac{1}{y}+\frac{1}{z}+\frac{1}{w}\right)$ is

EASY

Mathematics>Differential Calculus>Functions>Special Functions

${\log }_{10}0.001=$ _____

EASY

Mathematics>Differential Calculus>Functions>Special Functions

Find the value of ${\log }_5\sqrt{625}$

MEDIUM

Mathematics>Differential Calculus>Functions>Special Functions

If $4^{\mathrm{x}}-3^{\mathrm{x}-\frac{1}{2}}=3^{\mathrm{x}+\frac{1}{2}}\mathrm{ }-2^{2\mathrm{x}-1}$ then value of $\mathrm{x}$ is equal to

MEDIUM

Mathematics>Differential Calculus>Functions>Special Functions

The domain of the function $f\left(x\right)=\log \left(3x^2-4x+7\right)$ is

MEDIUM

Mathematics>Differential Calculus>Functions>Special Functions

The number of solutions of the equation ${\log }_4\left(x-1\right)={\log }_2\left(x-3\right)$ is ______.