The value of $\log \frac{1}{3}$ to the base $9$ is ______.

Important Questions on Exponentials and Logarithms

EASY

Quantitative Aptitude>Algebra>Exponentials and Logarithms>Logarithms

If ${\log }_{10}x+{\log }_{10}{x}^2=2{\log }_{10}x+1$, then what is the value of $x$?

MEDIUM

Quantitative Aptitude>Algebra>Exponentials and Logarithms>Logarithms

If ${\log }_{10}2 = 0.3010$ and ${\log }_{10}3=0.4771$, then the value of ${\log }_{100} (0.72)$ is equal to:

EASY

Quantitative Aptitude>Algebra>Exponentials and Logarithms>Logarithms

If $5^{x-1}={\left(2.5\right)}^{{{\log }_{10}}^5}$, then what is the value of $x$?

EASY

Quantitative Aptitude>Algebra>Exponentials and Logarithms>Logarithms

If $5^{\left(x-3\right)}=8$, then what is $x$ equal to?

MEDIUM

Quantitative Aptitude>Algebra>Exponentials and Logarithms>Logarithms

If ${\log }_5{\log }_8\left(x^2-1\right)=0$, then a possible value of $\mathrm{x}$ is

EASY

Quantitative Aptitude>Algebra>Exponentials and Logarithms>Logarithms

What is ${\log }_{10}31.25$ equal to?

MEDIUM

Quantitative Aptitude>Algebra>Exponentials and Logarithms>Logarithms

How many digits are there in ${\left(54\right)}^{10}$? $\left(\mathrm{Given} \mathrm{that} \log {10}^2=0.301 and \log {10}^3 = 0.477\right)$

EASY

Quantitative Aptitude>Algebra>Exponentials and Logarithms>Logarithms

What is the Value of ${\log }_{10}\left(\cos \mathrm{\theta }\right)+{\log }_{10}\left(\sin \mathrm{\theta }\right)+{\log }_{10}\left(\tan \mathrm{\theta }\right)+{\log }_{10}\left(\cot \mathrm{\theta }\right)+{\log }_{10}\left(\sec \mathrm{\theta }\right)+{\log }_{10}\left(\mathrm{cosec} \mathrm{\theta }\right)$?

MEDIUM

Quantitative Aptitude>Algebra>Exponentials and Logarithms>Logarithms

If ${\log }_{10}\left(8\right)=0.9031$, then what is the value of ${\log }_{10}\left(8000\right)+{\log }_{10}\left(600\right)$?

MEDIUM

Quantitative Aptitude>Algebra>Exponentials and Logarithms>Logarithms

What is the solution of the equation $x{\log }_{10}\left(\frac{10}{3}\right)+{\log }_{10}3={\log }_{10}(2+3^x)+x$?

EASY

Quantitative Aptitude>Algebra>Exponentials and Logarithms>Logarithms

For $0<\mathrm{m}<1$, which one of the following is correct?

MEDIUM

Quantitative Aptitude>Algebra>Exponentials and Logarithms>Logarithms

The inequality ${\log }_a\left\{f\right(x\left)\right\}<{\log }_a\left\{g\right(x\left)\right\}$ implies that

EASY

Quantitative Aptitude>Algebra>Exponentials and Logarithms>Logarithms

If $\log x=1.2500 \text{and} y=x^{\log x}$, then what is logy equal to?

EASY

Quantitative Aptitude>Algebra>Exponentials and Logarithms>Logarithms

If ${\log }_{10}\left(1995\right)$ $=3.3000$, then what is the value of ${\left(0.001995\right)}^{\frac{1}{8}}$?

MEDIUM

Quantitative Aptitude>Algebra>Exponentials and Logarithms>Logarithms

There are $n$ zeros appearing immediately after the decimal point in the value of ${\left(0.2\right)}^{25}$. It is given that the value of ${\log }_{10}2=0.30103$. The value of $n$ is

HARD

Quantitative Aptitude>Algebra>Exponentials and Logarithms>Logarithms

Let $f$ be a function defined on the set of all positive integers such that $f\left(xy\right)=f\left(x\right)+f\left(y\right)$ for all positive integers $x, y.$ If $f\left(12\right)=24$ and $f\left(8\right)=15$ , the value of $f\left(48\right)$ is

EASY

Quantitative Aptitude>Algebra>Exponentials and Logarithms>Logarithms

${\log }_{0.01}\left(10,000\right)=x$; Find the value of $x$?

MEDIUM

Quantitative Aptitude>Algebra>Exponentials and Logarithms>Logarithms

It is given that ${\log }_{10}2=0.301 \& {\log }_{10}3=0.477$. How many digits are there in $(108{)}^{10}?$

MEDIUM

Quantitative Aptitude>Algebra>Exponentials and Logarithms>Logarithms

The inequality ${\log }_2\frac{3x-1}{2-x}<1$ holds true for

EASY

Quantitative Aptitude>Algebra>Exponentials and Logarithms>Logarithms

The value of ${\left({\log }_{3}30\right)}^{-1}+{\left({\log }_{4}900\right)}^{-1}+{\left({\log }_{5}30\right)}^{-1}$ is