If 1/2 < logx < 2, then which of the following is true?

[lanieley]

A multiple choice question.

If 1/2 < logx < 2 then:

a) 10 ^1/2 < x <10^2
b)(1/2)^10 < x <(2)^10
c) 1/2 < x < 2
d) log1/2 < x < log2

 

[stapel]

If 1/2 < logx < 2 then....

What is the base of the logarithm? With no base specified,the notation could mean log-base-10 (the "common" log), log-base-2, or log-base-e (the "natural" log).

When you reply, please include your work and reasoning so far. Thank you!

Eliz.

 

[lanieley]

Hi Eliz(quick reply! )

I assume that it's log base 10, because wouldn't it be lnx if it was logbase e?

Well first I made a graph and shaded in where logx would be but other then that I don't' really know where to start. ^^;

I think the question is asking what is logx if it's between1/2 and 2.
That might mean 10^? = x
so ?= somewhere between 1/2 and 2.
Does x needed to be solved for this question?

I think I'm rambling... My answer key says that the answer is a but I don't know why.

but
log100=2 (10^2 =100)
and log?10 = 1/2 (10^1/2 = ?10)

 

[Deleted member 4993]

A multiple choice question.

If 1/2 < logx < 2 then:

a) 10 ^1/2 < x <10^2
b)(1/2)^10 < x <(2)^10
c) 1/2 < x < 2
d) log1/2 < x < log2

Certainly the fourth choice is not valid.

Then look at the fist choice. If you take log of each term - you get

log[10^(1/2)] < log (x) < log[10^2]

simplifying

1/2 < log(x) < 2

Your quest is over - however you should the other choices - just for practice.

 

[stapel]

I assume that it's log base 10, because wouldn't it be lnx if it was logbase e?

Sorry; no.

With no base specified, the notation could mean log-base-10 (the "common" log), log-base-2, or log-base-e (the "natural" log).

The "meaning" of "a log with no base" will vary with the context. :shock:

Eliz.