Question

Rewrite the logarithm log8(2) as an exponential expression then find the value of the logarithm

Answer 1

log8(2) = 1/3

Explanation:

I don't know if they mean this by an exponential expression but:

set x = log8(2), then

8^x = 8^(log8(2))

By logarithmic properties:

8^x = 2.

notice that 8 = 2^3.

By exponential properties:

8^x = (2^3)^x = 2^(3x)

So 2^(3x) = 2 = 2^1.

Comparing exponents gives:

3x = 1 <=> x = 1/3.

So log8(2) = 1/3.

Answer 2

exponential expression:

8ᵇ = 2

log8(2) = 0.333333333 or 1/3