#### Answer

$x=3$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
e^{6x}\cdot e^x=e^{21}
,$ use the laws of exponents to simplify the left side. Then drop the bases on both sides and equate the exponents. Use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Using the Product Rule of the laws of exponents which is given by $x^m\cdot x^n=x^{m+n},$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
e^{6x+x}=e^{21}
\\\\
e^{7x}=e^{21}
.\end{array}
Since the bases are the same, drop the bases and equate the exponents. That is,
\begin{array}{l}\require{cancel}
7x=21
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
x=\dfrac{21}{7}
\\\\
x=3
.\end{array}