Answer:
gives the solution
.
gives the solution
.
Step-by-step explanation:
I will solve both interpretations.
If we assume the equation is , then the following is the process:
Add 5 on both sides:
Simplify:
Now write an equivalent logarithm form:
Now using the change of base:
.
If we assume the equation is , then we use the following process:
Write an equivalent logarithm form:
Add 5 on both sides:
Use change of base formula:
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Explanations:
Part 1
For the first box, we use the log rule that log(A)+log(B) = log(A*B)
Then in the second box, we'll convert to exponential form. The logs are assumed to be base 10.
The third box then factors and uses the zero product property.
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Part 2
We check each solution generated in part 1.
Plugging x = 5/3 will lead to the same number on each side. Therefore, x = 5/3 is a true solution.
In contrast, plugging x = -2 leads to a false equation. Recall that the domain of y = log(x) is x > 0. This means we cannot replace x with negative numbers. The value x = -2 is extraneous.
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Part 3
There's not much to explain here that isn't already done so on the screenshot below.
