SOLUTION: Properties of logoritiris
I need help
Solve this equation
7. log7(3x+5)-log7(x-5)=log78
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Question 195165This question is from textbook algebra2
: Properties of logoritiris
I need help
Solve this equation
7. log7(3x+5)-log7(x-5)=log78
This question is from textbook algebra2
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The difference of the logs is the log of the quotient, i.e.:
 - \log_b(y) = \log_b\left(\frac{x}{y}\right))
From which you can simplify your LHS to:
 - \log_7(x-5) = \log_7\left(\frac{3x+5}{x-5}\right))
So:
 = \log_7{8})
Since two logs to the same base are equal if and only if their arguments are equal, you can now write:
Now all you have to do is solve the rational equation for x. Remember to check any potential solutions to ensure that they are in the domain of both the rational expression and of the log functions.
John
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