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# Properties of Logarithms

Directions: Using the integers 1 through 9, at most one time each, find the value of x that is closest to 0. Extension: Find more than one set of numbers that would make x = 0. ### Hint

How can you rewrite this expression using properties of logarithms?

Source: Claire Verti

## Creating Sequences

Directions: Using the digits 1-9, at most one time each, complete the first three terms …

1. Alexander Fischer

I love this question. Thank you for providing it! I would argue that log base six of eight ninths is the only correct answer however.

• Why do you think that log_6(8/9) is the only correct answer?

I’m having trouble seeing how that would be the case if log_6(8/9) and log_6(9/8) are opposites of one another.

2. 1/9 is closer to 1 than 1/8. Do we need to revise this answer???

• True, 1/9 is closer to 1 than 1/8, but with the logs an interesting difference happens:
log(8/9)=log(8)-log(9)
log(9/8)=log(9)-log(8)