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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 $6$.
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