Question:
The sum of the divisors of $2^4\cdot 3^3 \cdot 5^3$ is
The sum of the divisors of $2^4\cdot 3^3 \cdot 5^3$ is
Updated On: Jul 7, 2022
- $31 \times 40 \times 156$
- $30 \times 40 \times 150$
- $31 \times 40 \times 150$
- none of these
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Reqd. sum $=\frac{2^{5}-1}{2-1}. \frac{3^{4}-1}{3-1}\cdot\frac{5^{4}-1}{5-1}$
$=\left(31\right)\left(40\right)\left(156\right)$
Was this answer helpful?
0
0
Top Questions on Exponential and Logarithmic Functions
- Solve for \( x \): \( \log_2 (x-1) = 3 \).
- MHT CET - 2025
- Mathematics
- Exponential and Logarithmic Functions
- If $f : \mathbb{R}^+ \to \mathbb{R}$ is defined as $f(x) = \log_a x$ where $a>0$ and $a \neq 1$, prove that $f$ is a bijection. (R$^+$ is the set of all positive real numbers.)
- CBSE CLASS XII - 2025
- Mathematics
- Exponential and Logarithmic Functions
- If \( \log_2 3 = p \), express \( \log_8 9 \) in terms of \( p \):
- AP EAPCET - 2025
- Mathematics
- Exponential and Logarithmic Functions
- \( \int \sin^{-1}\left(\frac{x}{\sqrt{a+x}}\right) \, dx = \)
- AP EAPCET - 2025
- Mathematics
- Exponential and Logarithmic Functions
- Evaluate \[ \int \frac{1}{1 + x^2} \, dx = ? \]
- AP EAPCET - 2025
- Mathematics
- Exponential and Logarithmic Functions
View More Questions
Concepts Used:
Exponential and Logarithmic Functions
Logarithmic Functions:
The inverses of exponential functions are the logarithmic functions. The exponential function is y = ax and its inverse is x = ay. The logarithmic function y = logax is derived as the equivalent to the exponential equation x = ay. y = logax only under the following conditions: x = ay, (where, a > 0, and a≠1). In totality, it is called the logarithmic function with base a.
The domain of a logarithmic function is real numbers greater than 0, and the range is real numbers. The graph of y = logax is symmetrical to the graph of y = ax w.r.t. the line y = x. This relationship is true for any of the exponential functions and their inverse.
Exponential Functions:
Exponential functions have the formation as:
f(x)=bx
where,
b = the base
x = the exponent (or power)