Question

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

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asked 2021-05-08
Use the properties of logarithms to solve the following equation.
\(\log_{7}(x+2)=\log_{7}(14)−\log_{7}(x−3)\)

Answers (1)

2021-05-09

Step 1
The second question is opinion question and cannot be answered as per bartleby guidelines.
It is given that:
\(\log_{7}(x+2)=\log_{7}(14)−\log_{7}(x−3)\)
use the formula \(\log a−\log b=\log(\frac{a}{b})\) to get:
\(\log_{7}(x+2)=\log_{7}(\frac{14}{x-3})\)
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.

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