Question

Complete the input-output table for log4X. How would I solve this?

Answer 1

`x \to f(x)`

`0.25 \to -1`

`0.5 \to -0.5`

`1 \to 0`

`2 \to 0.5`

`4 \to 1`

`8 \to 1.5`

Explanation:

Given

`f(x) = log_4(x)`

`x = 0.5`

`f(x) = log_4(x)`

`f(0.5) = log_4(0.5)`

Apply law of logarithm

`f(0.5) = (log(0.5))/(log(4))`

Using a calculator, we have:

`f(0.5) = -0.5`

`x = 1`

`f(x) = log_4(x)`

`f(1) = log_4(1)`

Express 1 as 4^0

`f(1) = log_4(4^0)`

Apply law of logarithm

`f(1) = 0*log_4(4)`

`f(1) = 0`

`x = 2`

`f(x) = log_4(x)`

`f(2) = log_4(2)`

Apply law of logarithm

`f(2) = (log(2))/(log(4))`

Using a calculator, we have:

`f(2) = 0.5`

`x = 4`

`f(x) = log_4(x)`

`f(4) = log_4(4)`

`log_a(a) = 1`

So:

`f(4) = 1`

`x = 8`

`f(x) = log_4(x)`

`f(8) = log_4(8)`

Apply law of logarithm

`f(8) = (log(8))/(log(4))`

Using a calculator, we have:

`f(8) = 1.5`

So, the complete table is:

`x \to f(x)`

`0.25 \to -1`

`0.5 \to -0.5`

`1 \to 0`

`2 \to 0.5`

`4 \to 1`

`8 \to 1.5`