Exercise 2 Page 300

To solve the given exponential equation, note that we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal. 5^(2x) = 5^(x+1) ⇔ 2x = x+1Finally, we will solve the equation 2x = x+1 by subtracting x from both sides of the equation. 2x = x+1 ⇔ x = 1 To check our answer, we will substitute 1 for x in the given equation.

5^(2x) = 5^(x+1)

Substitute

x= 2

5^(2( 1)) ? = 5^(1+1)

MultByOne

a * 1=a

5^2 ? = 5^(1+1)

AddTerms

Add terms

5^2 ? = 5^2

CalcPow

Calculate power

25 = 25 ✓

Since substituting 1 for x in the given equation produces a true statement, x=1 is the solution to our equation.