Use logarithm properties to simplify numeric logarithmic expressions and estimate values.
Rewrite a numeric logarithm by factoring and expanding a product
Problem
How can you rewrite \(\log_2(40)\) as simpler known logarithms?
Big Picture
What this problem is really about
Useful logarithm expansion starts with purposeful factoring: expose the largest convenient power of the logarithm’s base and leave a simpler positive factor. The product law then separates those factors, allowing the exact-power piece to become an integer while the remaining logarithm stays intact. Splitting an argument as a sum would not support this move.
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