Question:
Approximate log base b of x, log_b(x).
Of course x can't be negative, and b > 1.
Answer:
f(x) = (-1/x + 1) / (-1/b + 1)
Step-by-step explanation:
log(1) is zero for any base.
log is strictly increasing.
log_b(b) = 1
As x descends to zero, log(x) diverges to -infinity
Graph of f(x) = (-1/x + 1)/a is reminiscent of log(x), with f(1) = 0.
Find a such that f(b) = 1
1 = f(b) = (-1/b + 1)/a
a = (-1/b + 1)
Substitute for a:
f(x) = (-1/x + 1) / (-1/b + 1)
f(1) = 0
f(b) = (-1/b + 1) / (-1/b + 1) = 1
Answer:
Her average speed is 48 miles per hour.
Step-by-step explanation:
We solve this question using a system of equations.
The speed equation is:

In which s is the speed, d is the distance, and t is the time.
Gabriella drives her car 320 miles and averages a certain speed.
So 
Then

If the average speed has been 6 miles less she could have traveled only 280 miles in the same length of time.
So, which s - 6, d = 280.

From the first equation:



Replacing:







Her average speed is 48 miles per hour.
The answer will be true
Have a nice day :)