Question

Use exponential form to evaluate log8(2)

Answer 1

Logarithm form is another way to express a number in exponential (exp.) form. log 8 (2) is the same as 8 (x) = 2 or in words, eight with exp. x equals two. If we take that equation and cube both sides, or raise each side to the power of 3, [8 (x)] with exp. 3 = 2 with exp. 3. This simplifies to 8 (3x) = 8. By definition, 8 is the same as 8 with exp. 1. So the equation is now 8 (3x) = 8 (1). This means 3x = 1. We can simplify to x = 1/3.

Answer 2

Answer:  $\frac{1}{3}$

Explanation:

let y = $log_{8} (2)$

whenever we transfer base from  log from one side to other it will remain be base after shifting to the other side.

Change log to exponent form $\log_xm=n\\m =x^{n}$

here we have n = y, m=2, x=8    by substituting the values

we will get

$8^{y} = 2$          (1)

we can write 8 in power of 2 that is $2^{3}$

we will rewrite the above equation (1) as

$2^{3y} = 2$

we can equate the power when base is same then we will get

3y = 1

then

$y=\frac{1}{3}$