Answer as an inequality: 
Answer in interval notation: 
Answer in words: Set of positive real numbers
All three represent the same idea, but in different forms.
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Explanation:
Any log is the inverse of an exponential equation. Consider a general base b such that f(x) = b^x. The inverse of this is 
For the exponential b^x, we cannot have b^x = 0. We can get closer to it, but we can't actually get there. The horizontal asymptote is y = 0.
Because of this, 
has a vertical asymptote x = 0 (recall that x and y swap, so the asymptotes swap as well). This means we can get closer and closer to x = 0 from the positive side, but never reach x = 0 itself.
The domain of is x > 0 which in interval notation would be . This is the interval from 0 to infinity, excluding both endpoints.
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The natural log function Ln(x) is a special type of log function where the base is b = e = 2.718 approximately.
So,
allowing all of what was discussed in the previous section to apply to this Ln(x) function as well.
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In short, the domain is the set of positive real numbers. We can't have x be 0 or negative.
An equation is formed of two equal expressions. The value of the constant of proportionality is 0.41.
<h3>What is an equation?</h3>
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given there exists a proportional relationship between the number of juice bottles bought, j, and the total cost in dollars and cents. Therefore,
c ∝ j
c = kj
As the relation is represented by the equation c=0.41j. Therefore, the value of the constant of proportionality is 0.41.
Learn more about Equation:
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Answer: 6.4 miles
Step-by-step explanation:
Lucinda lives 0.6 miles from the Park and Angie lives 10 times as far as this.
= 0.6 * 10
= 6 miles
Stacy lives 1/10 miles further than Angie;
= 6 + 1/10
= 6.1 miles
She lives 3/10 of a mile closer than Gabriel which means that Gabriel lives 3/10 of a mile further from the park than Lucinda;
= 6.1 + 3/10
= 6.4 miles
