1. Change the following exponential forms into logarithmic forms.
1. 2³ = 8         2. ³√(64) = 4          3.; (√2)⁸ = 16

Solution:

1. we know that if

a^x = n, then log _a n = x

therefore, if

2³ = 8, then log ₂ 8 = 3

2. ³√(64)

= (64)^1/₃ = 4

log ₆₄ 4 = 1/₃

3. (√2)⁸ = 16

log _√2 16 = 8

2. Change the following logarithmic forms into exponential forms:

1. log ₄ 16 = 2         2. log ₆ 36 = 2      3. log _a ³√(x) = 1/_y

Recall that if

log _a x = n, then aⁿ = x

Solution1:

log ₄16 = 2, 4² = 16

Solution 2:

log ₆ 36 = 2, 6² = 36

Solution 3:

log _a ³√(x) = 1/_y ,

a^1/_y = ³√(x)

a^1/_y = x^1/₃

2. Find log ₂ (log ₃ 81) = log ₃ X

Solution:

Let log ₃ 81 = n,

then 3ⁿ = 81,

3 ⁿ = 3⁴ ,

n = 4

so, in the given question,

log ₂ (log ₃81) reduces to log ₂ 4.

Now the question is

log ₂ 4 = log ₃ X…………………..(2)

again, let

log ₂ 4 = n,

then 2ⁿ = 4 = 2², so n = 2

writing n = 2 in (2), we get

2 = log ₃ X

So, 3² = X

X = 9

Now, we will learn simple laws of logarithms to solve above type of problems easily and in far fewer steps in the following pages.