If:
2a = 3
3b = 4
4c = 5
5d = 6
Then, find the value of a*b*c*d
Rewrite each as a logarithm and then use the change of base formula to rewrite each as log 2:
a = log2(3)
b= log3(4) = log2(4)/log2(3)
c= log4(5) = log2(5)/log2(4)
d= log5(6) = log2(6)/log2(5)
The product is a bunch of fractions, but everything reduced except log(2)6.
I show this to my student when we learn logarithm rules every year, except that I use two extra terms so the final answer is a round number: log2(8)=3. They love seeing how all the fractions reduce.
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Posted by Jer
on 2025-03-20 13:40:20 |
Slight variant solution
