Evaluate log base b of 10

Problem

(log_b)(10)

Solution

1. Identify the expression as a logarithm with an arbitrary base b and an argument of 10

2. Apply the change of base formula to rewrite the expression in terms of common logarithms (base 10 or natural logarithms (base e.

3. Use the formula (log_b)(a)=(log_k)(a)/(log_k)(b) where k is the new base.

4. Substitute a=10 and k=e to express the result using natural logarithms.

5. Simplify the numerator if using base 10 since (log_10)(10)=1

Final Answer

(log_b)(10)=ln(10)/ln(b)

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