Demonstrate two different ways to solve the equation 5^ (2x+1) = 25.

Step-by-step explanation:

Method 1: Taking the log of both sides ...

So take the log of both sides ...

5^ (2x + 1) = 25

log 5^ (2x + 1) = log 25 <- - use property: log (a^x) = x log a ...

(2x + 1) log 5 = log 25 <- - distribute log 5 inside the brackets ...

(2x) log 5 + log 5 = log 25 <- - subtract log 5 both sides of the equation ...

(2x) log 5 + log 5 - log 5 = log 25 - log 5

(2x) log 5 = log (25/5) <- - use property: log a - log b = log (a/b)

(2x) log 5 = log 5 <- - divide both sides by log 5

(2x) log 5 / log 5 = log 5 / log 5 <-- - this equals 1 ...

2x = 1

x=1/2

Method 2

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

2x+1=2

2x=1

x=1/2