No not all since for example 5.0 is in decimal form but is not a rational number
Answer:
(d) f(x) = log₆(x)
Step-by-step explanation:
If we use y in place of f(x), we see that ...
x = 6^y
Taking logs of both sides, we get ...
log(x) = y·log(6)
y = log(x)/log(6)
y = log₆(x) . . . . . . . using the change of base formula
f(x) = log₆(x)
_____
Or you can get there more directly using the relation between logs and exponentials:

Answer:
Step-by-step explanation:
Given that:
Mean μ= 100
standard deviation σ = 2.6
sample size n = 9
sample mean X = 100.6
The null hypothesis and the alternative hypothesis can be computed as follows:


The numerical value for the test statistics is :



z = 0.6923
At ∝ = 0.05

The critical value for the z score = 0.2443
From the z table, area under the curve, the corresponding value which is less than the significant level of 0.05 is 1.64
P- value = 0.244
c> If the true population mean is 101.3 ;
Then:



z = 0.808
From the normal z tables
P value = 0.2096
In the third quadrant, the tangent is positive.
tan(θ) = tan(arcsin(0.7660)) ≈ 1.1916