2.Let us now solve a few problems applying the logarithm formulas and concepts learned so far.

**1. Change the following exponential forms into logarithmic forms.**

**1. 2 ^{3} = 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

2^{3} = 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 a^{n} = x

* Solution1:*

log _{4}16 = 2, 4^{2} = 16

*Solution 2:*

log _{6} 36 = 2, 6^{2} = 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 3^{n} = 81,

3 ^{n} = 3^{4} ,

n = 4

so, in the given question,

log _{2} (log _{3}81) reduces to log _{2} 4.

Now the question is

log _{2} 4 = log _{3} X…………………..(2)

again, let

log _{2} 4 = n,

then
2^{n} = 4 = 2^{2}, so n = 2

writing n = 2 in (2), we get

2 = log _{3} X

So, 3^{2} = 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.