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

78.59 is the mean

step-by-step explanation:

y = 2x

step-by-step explanation:

if you divide each number in the sequence, you'll see that they all have a multiple factor of 2. each number in the series, and any other numbers which may continue, will be multiplied by 2. therefore, y is the next number in the sequence, and x is the current one, so, our formula will be y = 2x.