What is log x + log y - 2 log z written as a single logarithm?
1 answer:
Answer:
D) log (xy/z^2)
Step-by-step explanation:
The given expression is log x + log y - 2 log z
Here we use log rules to simplify this.
Product rule: log x + log y = log (xy)
Quotient rule : log x - log y = log(x/y)
Power rule: log(x^y) = y.log(x)
Using the product rule
log x + log y - 2 log z
= log(xy) - 2 log z
Use the power rule now.
= log(xy) - log z^2
Now we have to use the Quotient rule and simplify.
= log
Answer: D) log (xy/z^2)
Thank you.
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Answer:
We have the equation:
3x - 5y = 15
a) We want to create a table with at least 4 points.
To do this, first, let's write the equation as a function: We must isolate one of the variables. Let's isolate y.
5y = 3x - 15
y = (3/5)*x - 3.
Then we have a linear equation.
Now, we can input different values of x, and see what value takes y in each case, then in this way we can be sure that the points will be on the line.
x = 0.
y = (3/5)*0 - 3
y = -3
Then we have the point (0, -3).
x = 1.
y = (3/5)*1 - 3 = 3/5 - 15/5 = -12/5
y = -12/5
Then we have the point (1, -12/5)
x = 5
y = (3/5)*5 - 3 = 3 - 3 = 0
y = 0
then we have the point (5, 0)
x = 10
y = (3/5)*10 - 3 = 6 - 3 = 3
y = 3
Then we have the point (10, 3).
Now we can create the table
Below you can see a graph, where the blue dots are our 4 points, and the green line is the line that represents the equation.
