Because we have the same logarithm on each side, we need to have the argument on both sides, and from this, we will see that:
x = -3.
How to solve the logarithmic equation?
Here we want to solve the equation:
log₇(x - 4) = log₇(4x + 5)
Now, log₇(x) = ln(x)/ln(7) is a one-to-one function, meaning that each value in the range is given by a single value in the domain.
This means that the equation will only be true if the arguments in both logarithms are the same (because in both sides we have the base 7 logarithm).
Then we need to solve:
x - 4 = 4x + 5
-5 - 4 = 4x - x
-9 = 3x
-3 = x
So the solution for the given equation is:
x = -3
If you want to learn more about logarithms, you can read:
https://brainly.com/question/13473114
