23. $$ \log _{2}(3 x-4)=\log _{2} 5 $$

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To solve the equation:

$$
\log _{2}(3x - 4) = \log _{2} 5
$$

**Step 1: Understand the Property of Logarithms**

If $$\log_b A = \log_b B$$, then $$A = B$$, provided that $$A > 0$$ and $$B > 0$$. This property allows us to set the arguments of the logarithms equal to each other.

**Step 2: Set the Arguments Equal**

$$
3x - 4 = 5
$$

**Step 3: Solve for $$x$$**

$$
3x - 4 = 5
$$

Add 4 to both sides:

$$
3x = 5 + 4
$$
$$
3x = 9
$$

Divide both sides by 3:

$$
x = \frac{9}{3}
$$
$$
x = 3
$$

**Step 4: Verify the Solution**

It's essential to ensure that the arguments of the logarithms are positive:

$$
3x - 4 > 0
$$

Substitute $$x = 3$$:

$$
3(3) - 4 = 9 - 4 = 5 > 0
$$

Since the argument is positive, $$x = 3$$ is a valid solution.

**Final Answer:**
$$
x = 3
$$
$$ x = 3 $$

23. \( \log _{2}(3 x-4)=\log _{2} 5 \)

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