# How do you calculate # log 0.1 #?

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Let's think about this question in a different way than it's being asked - I find that sometimes students understand exponents and powers better than they understand logs.

The term

So the above and

are the same question - it's just that in that first one we need to solve for

So what do they equal?

Let's solve the exponent question first and then the statement of value will become clear:

At this point it'd be helpful to know that when we have a negative exponent, it means that we're talking about a fractional value and that the value that has the fractional exponent, to be positive, needs to swap its place in the fraction (so move to the denominator from the numerator, or vice versa).

So the expression

So

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