You're supposed to simplify these, but for the last one, isn't it simplified enough?
1 answer:
You might be interested in
Answer:
Step-by-step explanation:
So, there are two logarithmic identities you're going to need to know.
<em>Logarithm of a power</em>:
So to provide a quick proof and intuition as to why this works, let's consider the following logarithm:
Now if we raise both sides to the power of c, we get the following equation:
Using the exponential identity:
We get the equation:
If we convert this back into logarithmic form we get:
Since x was the basic logarithm we started with, we substitute it back in, to get the equation:
Now the second logarithmic property you need to know is
<em>The Logarithm of a Product</em>:
Now for a quick proof, let's just say:
Now rewriting them both in exponential form, we get the equations:
We can multiply a * c, and since b^x = a, and b^y = c, we can substitute that in for a * c, to get the following equation:
Using the exponential identity: , we can rewrite the equation as:
taking the logarithm of both sides, we get:
Since x and y are just the logarithms we started with, we can substitute them back in to get:
Now let's use these identities to rewrite the equation you gave
As you can see, this is a log of products, so we can separate it into two logarithms (with the same base)
Now using the logarithm of a power to rewrite the log(x^2) we get:
9514 1404 393
Answer:
see attached for a graph
x = 0.5 when y = 1
Step-by-step explanation:
The graph has a y-intercept of -1, which is halfway between 0 and -2. It goes up 4 units (2 vertical grid spaces) for 1 unit to the right (1 horizontal grid space). It seems to cross y = 1 at about x = 1/2.
x = 1/2 when y = 1.
