**Logarithmic form to exponential form :**

Here we are going to see how to convert the given question from logarithmic form to exponential form.

x = log_{a}b is the logarithmic form of the exponential form b ax = . In both the forms, the base is same.

Let us look into some examples to understand the concept given above.

**Example 1 :**

Change the following from logarithmic form to exponential form.

log _{4}64 = 3

**Solution :**

**Given logarithmic form : **

log _{4}64 = 3

**Exponential form :**

64 = 4^{3}

**Example 2 :**

Obtain the equivalent exponential form of the following

log_{16}2 = 1/4

**Solution :**

**Given logarithmic form :**

log_{16}2 = 1/4

**Exponential form :**

2 = 16^{1/4}

**Example 3 :**

Obtain the equivalent exponential form of the following

log_{5}(1/25) = -2

**Solution :**

**Given logarithmic form :**

log_{5}(1/25) = -2

**Exponential form :**

(1/25) = 5^{-2}

**Example 4 :**

Obtain the equivalent exponential form of the following

log_{10}0.1 = -1

**Solution :**

**Given logarithmic form :**

log_{10}0.1 = -1

**Exponential form :**

0.1 = 10^{-1}

**Example 5 :**

Obtain the equivalent exponential form of the following

log_{6}216 = 3

**Solution :**

**Given logarithmic form :**

log_{6}216 = 3

**Exponential form :**

216 = 6^{3}

**Example 6 :**

Obtain the equivalent exponential form of the following

log_{9}3 = 1/2

**Solution :**

**Given logarithmic form :**

log_{9}3 = 1/2

**Exponential form :**

3 = 9^{(1/2)}

**Example 7 :**

Obtain the equivalent exponential form of the following

log_{5}1 = 0

**Solution :**

**Given logarithmic form :**

log_{5}1 = 0

**Exponential form :**

1 = 5^{0}

**Example 8 :**

Obtain the equivalent exponential form of the following

log_{√3 }9 = 4

**Solution :**

**Given logarithmic form :**

log_{√3 }9 = 4

**Exponential form :**

9 = (√3)^{4}

**Example 9 :**

Obtain the equivalent exponential form of the following

log_{64 }(1/8) = -1/2

**Solution :**

**Given logarithmic form :**

log_{64 }(1/8) = -1/2

**Exponential form :**

(1/8) = 64^{(-1/2)}

**Example 10 :**

Obtain the equivalent exponential form of the following

log_{0.5 }8 = -3

**Solution :**

**Given logarithmic form :**

log_{0.5 }8 = -3

**Exponential form :**

8 = 0.5^{-3}

After having gone through the stuff given above, we hope that the students would have understood "Logarithmic form to exponential ".

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