$$ \operatorname { og } _ { 3 } ( x + 2 ) + \log _ { 3 } 10 = 3 $$

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
\log_3 (x + 2) + \log_3 10 = 3
$$

**Step 1: Combine the Logarithms**

Using the logarithm property $$\log_b A + \log_b B = \log_b (A \cdot B)$$, we can combine the two logarithmic terms:

$$
\log_3 \left((x + 2) \cdot 10\right) = 3
$$

**Step 2: Rewrite the Equation in Exponential Form**

The equation $$\log_3 C = 3$$ can be rewritten as:

$$
C = 3^3
$$

So,

$$
(x + 2) \cdot 10 = 27
$$

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

Divide both sides by 10:

$$
x + 2 = \frac{27}{10}
$$

$$
x = \frac{27}{10} - 2
$$

$$
x = \frac{27}{10} - \frac{20}{10}
$$

$$
x = \frac{7}{10}
$$

**Final Answer:**

$$
x = \frac{7}{10}
$$
$$ x = \frac{7}{10} $$

Upstudy AI Solution