Given: f(x)=log 5 x what is the value of f(125) and f(1/25)? Totally lost!
I assume you mean f(x) = log (5x), not log 5 * x. If this is the case, then
f(125) = log 600
and
f(1/25) = log (1/5)
If the base of the logs is 10, then
log 600 = 2.778..
To find the value of f(125) and f(1/25), we need to substitute these values into the function f(x) = log (5x).
Let's start with f(125):
f(125) = log (5 * 125)
To evaluate this logarithm, we can use the property that log(a * b) = log(a) + log(b). In this case, a = 5 and b = 125.
f(125) = log(5) + log(125)
Now, we need to find the values of log(5) and log(125). If the base of the logarithm is not specified, we can assume it is 10.
Now, log(5) is approximately 0.699 and log(125) is approximately 2.096.
f(125) = 0.699 + 2.096
Calculating this sum, we get:
f(125) ≈ 2.795
So, the value of f(125) is approximately 2.795.
Now, let's find f(1/25):
f(1/25) = log (5 * (1/25))
Using the same property as before, we can simplify this to:
f(1/25) = log(5) + log(1/25)
Again, let's find the values of log(5) and log(1/25):
log(5) ≈ 0.699
log(1/25) ≈ -1.398
Substituting these values into the equation, we get:
f(1/25) = 0.699 + (-1.398)
Calculating this sum, we get:
f(1/25) ≈ -0.699
So, the value of f(1/25) is approximately -0.699.