Evaluate log of 894.3

Problem

(log_)(894.3)

Solution

1. Identify the base of the logarithm. In most contexts, (log_)() without a specified base refers to the common logarithm (base 10).

2. Express the number in scientific notation to estimate the value.

894.3=8.943×10

3. Apply the logarithm product rule (log_)(a*b)=(log_)(a)+(log_)(b)

(log_)(8.943×10)=(log_)(8.943)+(log_)(10)

4. Simplify the integer part using the property (log_10)(10)=n

(log_)(10)=2

5. Calculate the mantissa (log_)(8.943) using a calculator or log table.

(log_)(8.943)≈0.95148

6. Add the components together to find the final value.

2+0.95148=2.95148

Final Answer

(log_)(894.3)≈2.95148

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