The solution of the given logarithmic equation is x = 28.1
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How to solve the logarithmic equation?</h3>
Here we have the logarithmic equation:
4*ln(x - 8) = 12
And we want to solve this for x.
Remember the relations:

First, we divide both sides by 4:

Then, if we apply the exponential equation to both sides of our equation, we get:

If you want to learn more about logarithmic equations:
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Answer:
Constant of variation: 1/4
Slope of the line: 1/4
Step-by-step explanation:
The constant of variation means the relationship between variables does not change. When we want to identify the constant of variation for an equation, it is helpful to refer to one of the following formulas: xy = k (inverse variation) or y/x = k (direct variation), where k is the constant of variation.
The slope formula states that m = (y2 -- y1) / (x2 -- x1). The slope formula can be read as "slope equals the second y coordinate minus the first y-coordinate over the second x-coordinate minus the first x-coordinate".
Answer: The number of solutions to the given equation is zero.
Step-by-step explanation: We are given to find the number of solutions to the following equation :

To find the number of solutions, we must solve the given equation.
The solution of equation (i) is as follows :
which can never be possible.
So, the given equation has no solution.
Thus, the number of solutions to the given equation is zero.
Answer:
x = 9.8
Step-by-step explanation:
They are same shape so we just get the ratio.
AB/JK = BC/KL
5 / 7 = 7 / x
5x = 49
x = 9.8