Solve for x: 3^2x−1=27

Question

.(1 point)
Responses

1
1

0
0

2
2

3

Answer 1

To solve the equation \( 3^{2x-1} = 27 \), we can first rewrite 27 as a power of 3. We know that:

\[ 27 = 3^3 \]

Now we can rewrite the equation:

\[ 3^{2x-1} = 3^3 \]

Since the bases are the same, we can set the exponents equal to each other:

\[ 2x - 1 = 3 \]

Now, solve for \( x \):

1. Add 1 to both sides: \[ 2x = 3 + 1 \] \[ 2x = 4 \]

2. Divide by 2: \[ x = \frac{4}{2} = 2 \]

Thus, the solution is:

\[ \boxed{2} \]