Questions: Solve the exponential equation by expressing each side as a power of the same base and then equating the exponents. 3^(3x-3) = 27 The solution set is

Solve the exponential equation by expressing each side as a power of the same base and then equating the exponents.

3^(3x-3) = 27

The solution set is

Transcript text: Solve the exponential equation by expressing each side as a power of the same base and then equating the exponents. \[ 3^{3 x-3}=27 \] The solution set is $\square$

Solution

Solution Steps

Step 1: Rewrite the Equation

We start with the exponential equation: \[ 3^{3x - 3} = 27 \] Next, we express $27$ as a power of $3$: \[ 27 = 3^3 \] Thus, we can rewrite the equation as: \[ 3^{3x - 3} = 3^3 \]

Step 2: Equate the Exponents

Since the bases are the same, we can equate the exponents: \[ 3x - 3 = 3 \]

Step 3: Solve for $x$

Now, we solve the equation for $x$: \[ 3x - 3 = 3 \] Adding $3$ to both sides gives: \[ 3x = 6 \] Dividing both sides by $3$ results in: \[ x = 2 \]