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Given #log(4)=0.6021#, #log(9)=0.9542#, and #log(12)=1.0792#, how do you find #log(0.06)#?

Answer 1

Anna Allen

Start by observing that:

#12/0.06 = 200#

Then ask yourself the question; "How do we divide by 200 using base 10 logarithms?"

In base 10, we divide by 100 by subtracting 2.

And divide by 2 by subtracting #1/2log(4)#

#log(0.06) = log(12)-2-1/2log(4)#

#log(0.06) = 1.0792-2-(0.6021)/2#

#log(0.06) = -1.2218#

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Answer 2

Elias Ackerman

You can use logarithmic properties to find log(0.06) by expressing 0.06 as a product of known logarithmic values. Specifically, you can express 0.06 as 6/100, which simplifies to 3/50. Then, you can use the property of logarithms that states log(ab) = log(a) + log(b). Thus, log(3/50) = log(3) - log(50). Next, you need to express 50 as a product of known logarithmic values. Since 50 = 5 × 10, log(50) = log(5) + log(10). Finally, use the given logarithmic values to substitute and solve for log(0.06).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.