Problem

Use properties of logarithms with the given approximations to evaluate the expression.

Use $\log _{b} 2=0.693$ and/or $\log _{b} 9=2.197$ to find $\log _{b} 18$.

Answer

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Answer

Final Answer: \(\boxed{2.89}\)

Steps

Step 1 :We are given that \(\log_b 2 = 0.693\) and \(\log_b 9 = 2.197\)

Step 2 :We can express \(\log_b 18\) as \(\log_b 2 + \log_b 9\) due to the property of logarithms that states \(\log_b (xy) = \log_b x + \log_b y\)

Step 3 :Substituting the given values, we get \(\log_b 18 = 0.693 + 2.197\)

Step 4 :Adding these values, we find that \(\log_b 18 = 2.89\)

Step 5 :Final Answer: \(\boxed{2.89}\)

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