Logs

Algebra Level 3

How many positive integers b have the property that log b 729 is a positive integer?

2 solutions

Matin Naseri
Mar 18, 2018

• $\text{}log_{3}729=9$

• $\text{}log_{9}729=3$

• $\text{}log_{27}729=2$

• $\text{}log_{729}729=1$

Exactly $\color{#20A900}{\boxed{4}}$ solutions exist for $\text{}log_{a}729=b$ such that $\text{}(b)$ be an positive integer.

$\mathfrak{Solved}$

Neeraj Bora
Apr 15, 2015

3,9,27,729

9^3 , 3^6 , 729^1 , 27^2

saurabh kumar - 5 years, 1 month ago