Use logarithm properties to simplify numeric logarithmic expressions and estimate values.
Determine whether a logarithm is positive, negative, or zero
Problem
Is \(\log_2(5)\) positive, negative, or \(\text{zero}\)?
Big Picture
What this problem is really about
For a logarithm with base greater than one, the sign comes from comparing the argument with one. One is the zero-exponent benchmark: arguments above it require positive exponents, arguments between zero and one require negative exponents, and the benchmark itself gives zero. Nearby powers can refine the check without a decimal.
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