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

Sinead Mcgee

Sinead Mcgee

Answered question

2021-05-08

Use the properties of logarithms to solve the following equation.
log7(x+2)=log7(14)log7(x3)

Answer & Explanation

Lacey-May Snyder

Lacey-May Snyder

Skilled2021-05-09Added 88 answers

Step 1
The second question is opinion question and cannot be answered as per bartleby guidelines.
It is given that:
log7(x+2)=log7(14)log7(x3)
use the formula logalogb=log(ab) to get:
log7(x+2)=log7(14x3)
Step 2
Cancel log from both sides to get:
x+2=14x3
(x+2)(x-3)=14
x2+2x3x6=14
x2x20=0
Step 3
Solve the quadratic equation as follows:
x25x+4x20=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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