# Use the properties of logarithms to solve the following equation. \log_{7}(x+2)=\log_{7}(14)−\log_{7}(x−3)

Use the properties of logarithms to solve the following equation.
${\mathrm{log}}_{7}\left(x+2\right)={\mathrm{log}}_{7}\left(14\right)-{\mathrm{log}}_{7}\left(x-3\right)$
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Step 1
The second question is opinion question and cannot be answered as per bartleby guidelines.
It is given that:
${\mathrm{log}}_{7}\left(x+2\right)={\mathrm{log}}_{7}\left(14\right)-{\mathrm{log}}_{7}\left(x-3\right)$
use the formula $\mathrm{log}a-\mathrm{log}b=\mathrm{log}\left(\frac{a}{b}\right)$ to get:
${\mathrm{log}}_{7}\left(x+2\right)={\mathrm{log}}_{7}\left(\frac{14}{x-3}\right)$
Step 2
Cancel log from both sides to get:
$x+2=\frac{14}{x-3}$
(x+2)(x-3)=14
${x}^{2}+2x-3x-6=14$
${x}^{2}-x-20=0$
Step 3
Solve the quadratic equation as follows:
${x}^{2}-5x+4x-20=0$
x(x-5)+4(x-5)=0
(x-5)(x+4)=0
x=5, -4
Hence the values of x are 5 and −4.