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We know that ratios can be shown with both fractions and colons.
20:705
or
It also looks like we can simplify this by dividing by 5.
20/5 = 4
705/5 = 141.
This means that for every 4 teachers, there are 141 students.
The ratio for teachers to students is:
4 : 141
The change of base formula looks like this:
log x
(log to the base b of ) x = ----------- (you could also use ln instead of log)
log b
log 40 1.602
Then (log to the base 7 of) 40 = ------------ = ------------- = 1.896 (answer)
log 7 0.8451
check (on calculator): 7^1.896 = 40.023 (close enough to 40 to verify
that this method "worked")
Answer:
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