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Challenge Answer 41


Solve the equation

By the definition of logarithm, we can write:

logy 0.001 = 2 - log y

From log base change ruleB a = (log a) / (log b), come:

(log 0.001) / (log y) = 2 - log y

We know that log 0.001 = -3, so:

-3 / (log y) = 2 - log y

-3 = 2 log y - log2 y
log2 y - 2 log y - 3 = 0 (2nd degree equation)

Applying Bhaskara's formula we find:

log y = 3 or log y = -1
y = 1000 or y = 0.1

Solution Set = {1000; 0.1}

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