Solve log₁₀3 + log₁₀4: Step-by-Step Logarithm Addition

To solve this problem, we will use the property of logarithms that allows us to combine the sum of two logarithms:

• Step 1: Identify the formula. We use the property $\log_b(x) + \log_b(y) = \log_b(x \cdot y)$ where both logarithms must have the same base.
• Step 2: Recognize the base. Here, both logarithms are in base 10: $\log_{10}3$ and $\log_{10}4$.
• Step 3: Apply the property. Add the two logarithms using the formula: $\log_{10}3 + \log_{10}4 = \log_{10}(3 \cdot 4)$.
• Step 4: Perform the multiplication. Compute $3 \cdot 4$ to get 12.
• Step 5: Express the result as a single logarithm: $\log_{10}12$.

Therefore, the expression $\log_{10}3 + \log_{10}4$ simplifies to $\log_{10}12$.