Find the value of ' $ m $ '
$3^{-2} \times 3^{2 m+1}=3^{3}$.
Given:
Given equation is $3^{-2} \times 3^{2 m+1}=3^{3}$.
To do:
We have to find the value of $m$.
Solution:
We know that,
$a^m \times a^n=a^{m+n}$
Therefore,
LHS $=3^{-2} \times 3^{2 m+1}$
$=3^{-2+2m+1}$
$=3^{2m-1}$
This implies,
$3^{2m-1}=3^3$
Comparing the powers on both sides, we get,
$2m-1=3$
$2m=3+1$
$2m=4$
$m=\frac{4}{2}$
$m=2$
The value of $m$ is $2$.
Related Articles
- If \( 1 \frac{1}{2} \times 2 \frac{2}{3} \times 3 \frac{3}{4} \times \ldots \times 199 \frac{199}{200}=\frac{1}{m}, \) then find the value of \( m \).
- $\frac{2 m}{3}+8=\frac{m}{2}-1$, find the value of $m$.
- Observe the following pattern.$2^{3}-1^{3}=1+2 \times 1 \times 3$$3^{2}-2^{3}=1+3 \times 2 \times 3$$4^{3}-3^{3}=1+4 \times 3 \times 3$Using this pattern, find the value of each of the following.$( a).\ 81^{3}-80^{3}$$( b).\ 100^{3}-99^{3}$
- Observe the following pattern\( (1 \times 2)+(2 \times 3)=\frac{2 \times 3 \times 4}{3} \)\( (1 \times 2)+(2 \times 3)+(3 \times 4)=\frac{3 \times 4 \times 5}{3} \)\( (1 \times 2)+(2 \times 3)+(3 \times 4)+(4 \times 5)=\frac{4 \times 5 \times 6}{3} \)and find the value of\( (1 \times 2)+(2 \times 3)+(3 \times 4)+(4 \times 5)+(5 \times 6) \)
- Solve the following:$m-\frac{m-1}{2}=1-\frac{m-2}{3}$
- Solve the following equation$2(m+1)-m=3(m+1)$
- Observe the following pattern:$1^{3}=1$$1^{3}+2^{3}=(1+2)^{2}$$1^{3}+2^{3}+3^{3}=(1+2+3)^{2}$Write the next three rows and calculate the value of $1^3 + 2^3 + 3^3 +…. + 9^3 + 10^3$ by the above pattern.
- Find the value of $4m^2 n^2 \times 7m^3$ when $m= \frac{-1}{2}$ and $n= 4$.
- The roots of the equation $x^{2} -3x-m( m+3) =0$, where m is a constant, are:$( A) m, m+3$$( B)-m, m+3$$( C)m, -(m+3)$$( D)-m,-(m+3)$
- Solve the following linear equation.\( m-\frac{m-1}{2}=1-\frac{m-2}{3} \).
- Prove that:\( \frac{3^{-3} \times 6^{2} \times \sqrt{98}}{5^{2} \times \sqrt[3]{1 / 25} \times(15)^{-4 / 3} \times 3^{1 / 3}}=28 \sqrt{2} \)
- If \( a \cos ^{3} \theta+3 a \cos \theta \sin ^{2} \theta=m, a \sin ^{3} \theta+3 a \cos ^{2} \theta \sin \theta=n \), prove that \( (m+n)^{2 / 3}+(m-n)^{2 / 3}=2 a^{2 / 3} \)
- Find the value of $a \times b$ if \( \frac{3+2 \sqrt{3}}{3-2 \sqrt{3}}=a+b \sqrt{3} \).
- Simplify: $2^{\frac{2}{3}}\times 2^{\frac{1}{3}}$.
- Simplify: $[ ( \frac{3}{2})^{-2}-( \frac{1}{3})^{2}]\times( \frac{5}{3})^{-2}$.
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies