## College Algebra (11th Edition)

$x=2$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $e^{8x}\cdot e^{2x}=e^{20} ,$ 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^{8x+2x}=e^{20} \\\\ e^{10x}=e^{20} .\end{array} Since the bases are the same, drop the bases and equate the exponents. That is, \begin{array}{l}\require{cancel} 10x=20 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} x=\dfrac{20}{10} \\\\ x=2 .\end{array}