$${{\mathtt{3}}}^{\left({{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{4}}\right)} = {{\mathtt{3}}}^{\left({\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}$$
It says to write the equation in terms of a common base (if not already) then use the property: b^x=b^y then x=y .
x^2 - 2x - 4 = 2x^2 +3x + 2
x^2 + 5x +6 =0
(x+2)(x+3)
x = -2 or x = -3
How did they combine?
+33661 What do you mean by "How did they combine?"? You have found the two values of x that make the original expression true.
x = -2
$${{\mathtt{3}}}^{\left({\left(-{\mathtt{2}}\right)}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}\left(-{\mathtt{2}}\right){\mathtt{\,-\,}}{\mathtt{4}}\right)} = {\mathtt{81}}$$
$${{\mathtt{3}}}^{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\left(-{\mathtt{2}}\right)}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}{\mathtt{\,\times\,}}\left(-{\mathtt{2}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)} = {\mathtt{81}}$$
x = -3
$${{\mathtt{3}}}^{\left({\left(-{\mathtt{3}}\right)}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}\left(-{\mathtt{3}}\right){\mathtt{\,-\,}}{\mathtt{4}}\right)} = {\mathtt{177\,147}}$$
$${{\mathtt{3}}}^{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\left(-{\mathtt{3}}\right)}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}{\mathtt{\,\times\,}}\left(-{\mathtt{3}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)} = {\mathtt{177\,147}}$$
.
+33661 What do you mean by "How did they combine?"? You have found the two values of x that make the original expression true.
x = -2
$${{\mathtt{3}}}^{\left({\left(-{\mathtt{2}}\right)}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}\left(-{\mathtt{2}}\right){\mathtt{\,-\,}}{\mathtt{4}}\right)} = {\mathtt{81}}$$
$${{\mathtt{3}}}^{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\left(-{\mathtt{2}}\right)}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}{\mathtt{\,\times\,}}\left(-{\mathtt{2}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)} = {\mathtt{81}}$$
x = -3
$${{\mathtt{3}}}^{\left({\left(-{\mathtt{3}}\right)}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}\left(-{\mathtt{3}}\right){\mathtt{\,-\,}}{\mathtt{4}}\right)} = {\mathtt{177\,147}}$$
$${{\mathtt{3}}}^{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\left(-{\mathtt{3}}\right)}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}{\mathtt{\,\times\,}}\left(-{\mathtt{3}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)} = {\mathtt{177\,147}}$$
.
