# SOLVE EQUATIONS WITH VARIABLE EXPONENTS

## About "Solve equations with variable exponents"

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.

## Solve equations with variable exponents - Examples

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 ==> 4³

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 2³.

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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