Question

Difficulty on the Reihman scale of really tough problems: 8/10 (+6 pts)

The Reihman acidity scale uses a logarithmic scale of base 37. Something that is a "1" is 37
times more acidic than a "2". Mr. Reihman mixes 1 gallon of something that is a "3" on the
Reihman scale and 1 gallon of something that is a "6" on the Reihman scale. What value would
this new mixture have on the Reihman scale? Show all work.

Answer 1

Explanation:

The Reihman scale measures acidity using a logarithmic scale of base 37, where a difference of 1 on the scale represents a 37-fold difference in acidity. In other words, something that is a "1" on the Reihman scale is 37 times more acidic than something that is a "2" on the scale.

To find the value of the mixture of 1 gallon of something that is a "3" on the Reihman scale and 1 gallon of something that is a "6" on the Reihman scale, we can use the following formula:

log37 (x) = (log37 (3) + log37 (6)) / 2

where x is the value of the mixture on the Reihman scale.

First, we need to find the logarithms of 3 and 6 to base 37:

log37 (3) = 0.3008

log37 (6) = 0.4771

Then, we can plug these values into the formula and simplify:

log37 (x) = (0.3008 + 0.4771) / 2

log37 (x) = 0.38895

Finally, we can solve for x by taking 37 to the power of 0.38895:

x = 37^(0.38895)

x = 2.7137

Therefore, the value of the mixture of 1 gallon of something that is a "3" on the Reihman scale and 1 gallon of something that is a "6" on the Reihman scale is approximately 2.7137 on the Reihman scale.