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

Sinead Mcgee 2021-05-08 Answered
Use the properties of logarithms to solve the following equation.
log7(x+2)=log7(14)log7(x3)
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Lacey-May Snyder
Answered 2021-05-09 Author has 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.

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions