Evaluate log of 35

Problem

(log_)(35)

Solution

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

2. Apply the product rule for logarithms. Since 35=5×7 the expression can be rewritten as the sum of two logarithms.

(log_)(35)=(log_)(5×7)

(log_)(35)=(log_)(5)+(log_)(7)

3. Substitute the approximate values for the common logarithms of 5 and 7.

(log_)(5)≈0.69897

(log_)(7)≈0.84510

4. Calculate the sum of the two values to find the final result.

0.69897+0.84510=1.54407

Final Answer

(log_)(35)≈1.54407

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