**Solve equations with variable exponents :**

**Step 1 :**

On both sides first we have to simplify using exponent rules.

**Step 2 :**

After rewriting exponential equations with same base on both sides, we can compare the powers. Because if two bases are same on both sides, then their powers are also equal.

**Step 3 :**

Based on the above rule, we can find the value of the variable.

**Example 1 :**

Find the value of m

**Solution :**

**5^m/5^(-3) = 5^5**

**5^m x 5^3 = 5^5**

**5^(m + 3) = 5^5**

**On both sides, we have the same base**

**m + 3 = 5**

**Subtracting 3 on both sides, we get**

**m + 3 - 3 = 5 - 3**

**m = 2**

**Example 2 :**

Find the value of m

**Solution :**

**In order to make the bases same on both sides, we have to split 64 as the multiple of 4.**

**64 = 4 x 4 x 4 ==> 4**³

4^m = 4^3

Since the base on both sides are equal, we can compare the powers.

m = 3

Hence the value of m is 3.

**Example 3 :**

Find the value of m

**Solution :**

**We can write 8 as 2 x 2 x 2 that is 2**³.

2^[3(m-3)] = 1

But in the right hand side, we have 1. We can write this 1 as any number raised to the power zero.

2^(3m-9) = 2^0

3m-9 = 0

Adding 9 on both sides, we get

3m - 9 + 9 = 0 + 9

3m = 9

dividing 3 on both sides, we get

m = 3

**Example 4 :**

Find the value of m

**Solution :**

**Since we have power raised to another power, we have to multiply both powers.**

**a^(3m) = a^9**

**On both sides we have the same base, so we can compare their powers**

**3m = 9**

**Dividing by 3 on both sides.**

**m = 3**

**Example 5 :**

Find the value of m

**Solution :**

**Since we have the same base on both sides, we can compare the powers.**

**2m + 12 = 0**

**Subtract 12 on both sides**

** 2m + 12 - 12 = 0 - 12**

** 2m = -12**

**divide by 2 on both sides**

** m = -6**

After having gone through the stuff given above, we hope that the students would have understood "Solve equations with variable exponents".

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