Q 90.

Solve the equation.

$\log_{3} (3 x - 2) = 2$

Verified

Answer

The solution to the equation, $\log_{3} (3 x - 2) = 2$ is, $x = \frac{11}{3}$ .

1Step 1. Given Information

The given equation to be solved is $\log_{3} (3 x - 2) = 2$ .

2Step 2. Formula used

Rule of change from logarithm to exponents:

$\log_{a} b = y \Rightarrow a^{y} = b$

3Step 3. Finding Solution

The given equation is $\log_{3} (3 x - 2) = 2$ .

Use rule of change from logarithm to exponents:

$\log_{3} (3 x - 2) = 2 3 x - 2 = 3^{2} 3 x = 9 + 2 x = \frac{11}{3}$

The solution to the given equation is, $x = \frac{11}{3}$ .