Question

Explain why log3 8 cannot be simplified to an integer value. A. There is no integer n such that 8 raised to the nth power equals 3. B. There is no integer n such that n raised to the eighth power equals 3. C. There is no integer n such that n raised to the third power equals 8. D. There is no integer n such that 3 raised to the nth power equals 8

Answer 1

Using the logarithm definition, it is found that the correct option regarding why $\log_{3}{8}$ cannot be simplified to an integer value.

C. There is no integer n such that n raised to the third power equals 8.

What is the logarithm function?

It is defined by:

$y = \log_{b}{x}$

It means that:

$b^y = x$

In this problem, the given logarithm is:

$\log_{3}{8}$

The equivalent exponential equation would be:

$3^n = 8$

However, $3^1 = 3, 3^2 = 9$, hence there is no integer n such that n raised to the third power equals 8 and option C is correct.

More can be learned about logarithms at https://brainly.com/question/2528611