How do you write log0.001=xlog0.001=x in exponential form?

2 Answers
anor277
Oct 26, 2015

If we're using base 1010, and I assume we are, loglog (0.001)(0.001) == -3−3. Why?

Explanation:

When we write log_ab = clogab=c, we are asking to what power we raise the base aa to get cc. Here, a^c = bac=b.

Here the base is 1010. So in fact we are asking to what power we raise 1010 to get 0.0010.001. This is clearly -3−3, because 10^-310−3 == 1/10^31103 == 1/100011000 == 0.0010.001. Apologies if have not grasped your question.

EZ as pi
Sep 24, 2016

log_10 0.001 = x " "hArr " "10^x= 0.001log100.001=x ⇔ 10x=0.001

Explanation:

Log form and exponential form are two ways to say the same thing.
They are interchangeable..

log_a b = c " "hArr" "a^c = blogab=c ⇔ ac=b

In this case we have

log_10 0.001 = x " "hArr " "10^x= 0.001log100.001=x ⇔ 10x=0.001

The question being asked in each form, is ....

"To what power must 10 be raised to give 0.001?"

To change from one to the other, remember..
"The base stays the base and the other two change around"

The answer for x can be found from:

10^x = 0.001 = 1 xx 10^-310x=0.001=1×10−3

x = -3x=−3

log_10 0.001 = -3 " " or " "10^-3 = 0.001log100.001=−3 or 10−3=0.001

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