Solve the following equations:
$ 3^{x+1}=27 \times 3^{4} $

Given:

\( 3^{x+1}=27 \times 3^{4} \)

To do: 

We have to solve the given equation.

Solution:

We know that,

$(a^{m})^{n}=a^{m n}$

$a^{m} \times a^{n}=a^{m+n}$

$a^{m} \div a^{n}=a^{m-n}$

$a^{0}=1$

Therefore,

$3^{x+1}=27 \times 3^{4}$

$=3^3\times3^4$

$=3^{3+4}$

$=3^{7}$

Comparing both sides, we get,

$x+1=7$

$x=7-1$

$x=6$

The values of $x$ is $6$.    

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

99 Views

Kickstart Your Career

Get certified by completing the course

Get Started