Solve the equation. If necessary, round to thousandths.
3^(2x + 1) = 27
my bad supposed to say algebra 2
3^(2x+1) = 3^3
2x+1 = 3
2x=2
x=1
Substitute (2x + 1) for y.
3^y = 27
y = 3
Back-substitute.
2x + 1 = 3
x = 1
To solve the equation 3^(2x + 1) = 27, we need to isolate the variable x. Here's the step-by-step process to find the solution:
Step 1: Rewrite both sides using the same base. Since 27 can be written as 3^3, we have:
3^(2x + 1) = 3^3
Step 2: Set the exponents equal to each other. Since the bases are the same, we can equate the exponents:
2x + 1 = 3
Step 3: Solve for x.
Subtract 1 from both sides of the equation:
2x = 3 - 1
2x = 2
Step 4: Divide by 2 on both sides to solve for x:
x = 2/2
x = 1
Therefore, the solution to the equation 3^(2x + 1) = 27 is x = 1.