Question

I have the steps, but I don't understand them.
Solve for 'x' in this exponential equation (see image):

Answer 1

\(\bf 7^{{\color{brown}{ x+1}}}-7^x=14406
\\ \quad \\
7^{\color{brown}{ x}}\cdot 7^{\color{brown}{ 1}}-7^x=14406
\\ \quad \\
common\ factor
\\ \quad \\
{\color{purple}{ 7^x}}\cdot 7^{\color{brown}{ 1}}-{\color{purple}{ 7^x}}=14406\implies 7^x(7^1-1)=14406
\\ \quad \\
7^x(6)=14406\implies 7^x=\cfrac{\cancel{ 14406}}{\cancel{ 6}}\implies 7^x=2401\qquad {\color{brown}{ 2401=7^4}}
\\ \quad \\
7^{\color{brown}{ x}}=7^{\color{brown}{ 4}}\qquad {\color{brown}{ x=4}}\)