Use logarithm properties to simplify numeric logarithmic expressions and estimate values.
Approximate a numeric logarithm by change of base to stated precision
Problem
Evaluate \(\log_{7}(30)\) by change of base. Give the quotient, the value rounded to \(\text{four}~\text{decimal}~\text{places}\), and a benchmark-power check.
Big Picture
What this problem is really about
Change of base places the logarithm of the argument over the logarithm of the original base, with the same calculator logarithm used in both places. Keep the full quotient until the requested final rounding. Neighboring powers of the original base provide a separate interval check that can catch a reversed ratio or an implausible decimal.
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