Question

Express the following in Exponential form:
i) $\log_{0.5} 0.125 = 3$
ii) $\log_{2} \frac{1}{4} = -2$

Answer 1

Answer:

i) (0.5)³ = 0.125

ii)(1/2)⁻² = 1/4

Step-by-step explanation:

Hi,  

If y = aˣ, then we define x as logₐy  (or)

If x = logₐy , then y = aˣ

Here , a > 0 and a ≠ 1 , a is called the base of the  

logarithm.

i) Given that log₀.₅ 0.125 = 3

Using the definition of logarithm,

we can rewrite as

0.125 = (0.5)³ (or)

(0.5)³ = 0.125

(ii)Given that log₁₍₂1/4 = -2

Using the definition of logarithm,

we can rewrite the above as

1/4 = (1/2)⁻² (or)

Re-arranging the terms, we get

(1/2)⁻² = 1/4

Hope, it helps !