Evaluate 3 log of 10^2

Problem

3*(log_)(10)

Solution

1. Identify the expression as a common logarithm, where (log_)(x) refers to (log_10)(x)

2. Apply the power rule of logarithms, which states that (log_b)(an)=n*(log_b)(a)

3. Move the exponent inside the logarithm to the front as a multiplier.

3⋅2*(log_)(10)

4. Simplify the multiplication of the constants.

6*(log_)(10)

5. Evaluate the logarithm, noting that (log_10)(10)=1

6⋅1

6. Calculate the final product.

6

Final Answer

3*(log_)(10)=6

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