Evaluate log of 18

Problem

(log_)(18)

Solution

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

2. Apply the product rule for logarithms, (log_)(a*b)=(log_)(a)+(log_)(b) by factoring 18 into its prime factors: 18=2⋅3

3. Expand the expression using the properties of logarithms.

(log_)(18)=(log_)(2⋅3)

(log_)(18)=(log_)(2)+(log_)(3)

4. Apply the power rule for logarithms, (log_)(an)=n*(log_)(a) to the second term.

(log_)(18)=(log_)(2)+2*(log_)(3)

5. Substitute the approximate values for common logarithms: (log_)(2)≈0.3010 and (log_)(3)≈0.4771

(log_)(18)≈0.3010+2*(0.4771)

6. Calculate the final numerical value.

(log_)(18)≈0.3010+0.9542

(log_)(18)≈1.2552

Final Answer

(log_)(18)≈1.2552

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