Use logarithm properties to simplify numeric logarithmic expressions and estimate values.
Estimate which two consecutive integers a logarithm lies between
Problem
Use consecutive powers of \(2\) to locate \(\log_{2}(20)\) between \(\text{two}~\text{consecutive}~\text{integers}\).
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What this problem is really about
Treat the logarithm as an unknown exponent and bracket its argument between consecutive powers of the base. Because a base greater than one produces an increasing exponential function, the exponents on those neighboring powers become the bounds for the logarithm. This locates the value exactly enough without calculating a decimal.
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