Question

Find the value of x in the following:

log₁₀ x = log₁₀ 2 + 2

Answer 1

Given: log₁₀ x = log₁₀ 2 + 2

Step-wise calculation:

1. Note 2 = log₁₀ 100

Use log addition: 

log_a u + log_a v = log_a (uv)

2. log₁₀ x = log₁₀ 2 + 2

= log₁₀ 2 + log₁₀ 100

= log₁₀ (2 × 100) 

= log₁₀ 200

3. Therefore, since log₁₀ is one-to-one and x > 0

x = 200