What is the logarithmic function modeled by the following table? x f(x) 9 2 27 3 81 4

The logarithmic function modeled by the given table:

f(x) = log₃x

Step-by-step explanation:

Given Table:

x     f(x)

9     2

27    3

81    4

We can see that x increases as powers of 3. And f(x) is the power.

We assume that f(x) = log₃x

Checking using the table:

for x = 9

f(x) = log₃9 = 2

for x = 27

f(x) = log₃27 = 3

for x = 81

f(x) = log₃81 = 4

Hence proved.  

Required logarithmic function is :

Step-by-step explanation:

Given that table for the logarithmic function is:

xf(x)

92

273

814

which can be rewritten as:

xf(x)

3^22

3^33

3^44

Which are basically powers of 3

Hence required logarithmic function is :

Required logarithmic function is :

Step-by-step explanation:

We have been fiven that table for the logarithmic function is:

xf(x)

92

273

814

which can be rewritten as:

xf(x)

3^22

3^33

3^44

Which are basically powers of 3

So we can use logarithmic function as

Hence required logarithmic function is :

The answer is A. f(x) = log4x

The logarithmic function modeled by the table would be

So it would seem to be answer B.

Log_2 8 = 3 (because 2^3 = 8

log_2 16 = 4

log_2 32 = 5

So its B

option 1.



x      f(x)

4      log (4) 4 = 1 ... because 4^1 = 4

16    log(4) 16 = 2 .... because 4^2 = 16

64    log (4) 64 = 3 .... because 4^3 = 64

So we need to come up with a function that when we plug x into it, it gives us    f(x). Logarithims ask: what exponent do I need to put on b (see the diagram to see what b is) to make it equal x. In the diagram below y is our f(x).

So we have logb (x) = f(x), we need to find what b is. Well the values look like 5 then 5 squared, then 5 cubed etc. So b=5.

To test this put one of the exponents (f(x)-values) on b and see if it equals the x value next to it in the table.

The answer is:

log 5 x = f(x)

The answer would be the following: f(x)=5^x