**Introduction :**

Exponents are the important concept in mathematical algebra. Exponentsare nothing but the power value of the variable. These exponents are both used in algebraic expressions and equations. In polynomials exponents are called as degrees. In this topic we have to learnt about how to solving for unknown exponents with example problems.

## Brief study about Solving for unknown exponents with suitable examples

**Example 1:**

**Solving for unknown exponents for the following algebraic equation 6**^{x} = 1296

**Solution:**

The given algebraic equation 6^{x} = 1296

Here x is the exponent value, now we have to find the value for x, for this we can write 1296 = 6 x 6 x 6x 6

That is 6^{4} = 6 x 6 x 6 x 6

Now we can write 6 x 6 x 6 x 6 = 6^{4}, then we can get the following equation of the form,

6^{x} = 6^{4}

Now the base value is equal so we have to directly cancel the power values, then we have to get

x=4

This is the solution of the given algebraic equation 6^{x} = 1296

**Example 2:**

**Solving for unknown exponents for the following algebraic equation 5**^{h} -1 =3124

**Solution:**

The given algebraic equation 5^{h} -1 =3124

First we have to adding the value 1 on both sides, then we can get,

5^{h} -1+1 =3124+1

That is 5^{h} =3125

Here h is the exponent value, now we have to find the value for h, for this we can write 3125 = 5 x 5 x 5 x 5 x 5

That is 5^{5} = 5 x 5 x 5 x 5 x 5

Now we can write 5 x 5 x 5 x 5 x 5="55, then we can get the following equation of the form,

5^{h} = 5^{5}

Now the base value is equal so we have to directly cancel the power values, then we have to get

h=5

This is the solution of the given algebraic equation 5^{h} -1 =3124

These are the good examples of solving for unknown exponents.