The price of an item was reduced 25% to $30. What was the original price of the item
1 answer:
You might be interested in
<em>Solve: </em>
Start by isolating the x-variable as much as you can:
Now, if we take the log with base 13 of both sides, then the left hand side will cancel out really easily. This is based on the concept of inverse operations. For example, when we take the square of a square root, we get our initial value. This is because the two operations are inverses of each other, and basically undoes each other.
Logarithms and exponentials are the inverse operations of each other. If we want to extrapolate the power of an exponential, we take the logarithmic function of it, and vice versa.
In this case, we are saying what power of '13' will produce us with 13ˣ, and the only answer will be x itself.
Start by isolating the x-variable as much as you can:
Now, if we take the log with base 13 of both sides, then the left hand side will cancel out really easily. This is based on the concept of inverse operations. For example, when we take the square of a square root, we get our initial value. This is because the two operations are inverses of each other, and basically undoes each other.
Logarithms and exponentials are the inverse operations of each other. If we want to extrapolate the power of an exponential, we take the logarithmic function of it, and vice versa.
In this case, we are saying what power of '13' will produce us with 13ˣ, and the only answer will be x itself.
First, it would be good to know that the area bounded by the curve and the x-axis is convergent to begin with.
Let
, so that 
, and the integral is equivalent to
The integrand is continuous everywhere except
, but that's okay because we have 
. This means the integral is convergent - great! (Moreover, there's a special function designed to handle this sort of integral, aptly named the "sine integral function".)
Now, to compute the volume. Via the disk method, we have a volume given by the integral
By the same substitution as before, we can write this as
The half-angle identity for sine allows us to rewrite as
and replacing
, 
, we have
Like the previous, this require a special function in order to express it in a closed form. You would find that its value is
where
is the Euler-Mascheroni constant and 
denotes the cosine integral function.
Let
The integrand is continuous everywhere except
Now, to compute the volume. Via the disk method, we have a volume given by the integral
By the same substitution as before, we can write this as
The half-angle identity for sine allows us to rewrite as
and replacing
Like the previous, this require a special function in order to express it in a closed form. You would find that its value is
where