# How do you solve 6^(x+2)=14^(x-3)?

Dec 30, 2017

$x \approx 13.57$

#### Explanation:

If ${6}^{x + 2} = {14}^{x - 3}$

then
$\textcolor{w h i t e}{\text{XX}} {6}^{x} \cdot {6}^{2} = {14}^{x} \cdot \frac{1}{{14}^{3}}$

$\textcolor{w h i t e}{\text{XX}} \frac{{14}^{x}}{{6}^{x}} = {6}^{2} \cdot {14}^{3}$

$\textcolor{w h i t e}{\text{XX}} {\left(\frac{7}{3}\right)}^{x} = 98784$

$\textcolor{w h i t e}{\text{XX}} x = {\log}_{\frac{7}{3}} 98784 \approx 13.57357421$
(...and, yes, I used a spreadsheet function to evaluate this)