Prove that 2log10+ 2log10-²- 1/3log5-³ +1/2log4=3

To prove that the given expression simplifies to 3, let's break down each logarithmic term and simplify step by step.

### Given Expression:
\[
2\log 10 + 2\log 10^{-2} - \frac{1}{3}\log 5^{-3} + \frac{1}{2}\log 4
\]

### Step 1: Simplify each logarithmic term

1. **First Term**: \(2\log 10\)

   Using the property

Learn how to prove the expression 2log10 + 2log10^-2 - 1/3log5^-3 + 1/2log4 = 3 step-by-step using logarithm properties. This problem involves advanced logarithmic concepts suitable for advanced high school and above.

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