Summing to One
$$\log_3 3=1$$
$$\log_9 3+ \log_9 3 =1$$
$$\log_{27} 3 + \dots = 1$$
How many $\log_{81} 3$ do you need to add together to make one?
Can we choose integers $x$ and $y$ so that:
$$\log_6 x +\log_6 y =1?$$
How many different ways are there to do this?
How about using $\log_{12}$?
How about using $\log_{24}$?
Underground Mathematics is hosted by Cambridge Mathematics. The project was originally funded by a grant from the UK Department for Education to provide free web-based resources that support the teaching and learning of post-16 mathematics.
Visit the site at undergroundmathematics.org to find more resources, which also offer suggestions, solutions and teacher notes to help with their use in the classroom.
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