Question

State, true or false : log₂ 8 = 3 and log₈ = 2 = ${\displaystyle \frac{1}{3}}$

Answer 1

Consider the equation
log₂8 = 3
⇒ 2³ = 8                                ....(1)
Now consider the equation
log₈2 = ${\displaystyle \frac{1}{3}}$
⇒ ${\displaystyle 8^{\frac{1}{3}}=2}$

⇒ ${\displaystyle {\left(2^3\right)}^{\frac{1}{3}}=2}$                ...(2)

Both the equations (1) and (2) are correct.
Thus the given statements, log₂8 = 3 and log₈2 = ${\displaystyle \frac{1}{3}}$ are true.