Solving for unknown exponents

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 6x = 1296

Solution:

The given algebraic equation 6x = 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 64 = 6 x 6 x 6 x 6

Now we can write 6 x 6 x 6 x 6 = 64, then we can get the following equation of the form,

6x = 64

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 6x = 1296


Example 2:

Solving for unknown exponents for the following algebraic equation 5h -1 =3124

Solution:

The given algebraic equation 5h -1 =3124

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

5h -1+1 =3124+1

That is 5h =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 55 = 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,

5h = 55

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 5h -1 =3124

These are the good examples of solving for unknown exponents.