use exponential form to evaluate log_8 2 show all steps

Answer 1

To evaluate log_8 2, we can convert it to exponential form.

Let's assume that log_8 2 = x.

According to the definition of logarithm, we have:

8^x = 2

To solve for x, we can rewrite 8 as a power of 2:

(2^3)^x = 2

Using the property of exponents, we can multiply the exponents:

2^(3x) = 2

Now, since the bases of both sides are the same, we can equate the exponents:

3x = 1

Dividing both sides by 3:

x = 1/3

Therefore, log_8 2 = 1/3.