Why the answer to this problem 4^(5x-3)=1 is 3/5?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

You want to know why x = 3/5 is a solution for 4^(5x-3) = 1.

Now in 4^(5x-3) = 1, the solution of x is a value that if substituted for x makes the right hand side equal to the left hand side.

If we substitute x = 3/5 in the left hand side, we get

4^(5x-3)

=> 4^(5*(3/5)-3)

=> 4^(3 - 3)

=> 4^0

=> 1

This is equal to the right hand side.

Therefore we know that x = 3/5 is a solution for the equation  4^(5x-3) = 1.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

4^(5x-3) = 1.

To solve this write 1  4^0 on the right.

So the equation is  4^(5x-3) = 4^0.

Therefore 5x-3 =  0, as  a^m = a^n, then  m = n.

5x = 3.

5x = 3.

x = 3/5.

Therefore x= 3/5.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Let's see how to get this answer. First, we'll re-write the equation, substituting 1 by 4^0, in this way creating matching bases both sides.

4^(5x-3) = 4^0

Since we have matching bases, we can apply one to one property:

5x - 3 = 0

We'll add 3 both sides:

5x - 3 + 3 = 3

5x = 3

We'll divide by 5:

x = 3/5

So, the answer 3/5 is the value of x that makes the identity to be true.

4^(5*3/5-3) = 1

4^(3-3) = 4^0

4^0 = 4^0 true for x = 3/5

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