How do you determine values for a and b that satisfy the double inequality 3<log_a(b)<43<loga(b)<4?

1 Answer
MrsRudolph221
Jan 21, 2017

In base a, your number must be between a^3a3 and a^4a4.

Explanation:

For example, if your base was 10, your numbers would be between 1000 and 10,000. In interval notation, (1000,10000).
Check: log_10(1234)~~3.09log10(1234)≈3.09

In base 2, they should be between (8,16).
Check: log_2(14)~~3.81log2(14)≈3.81

Try any other base to make sure!

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