Log Question

Question

Log Question

anonymous · Answer

$$\log_{2}(2x+5)<0 $$

anonymous · Answer

solve for x

anonymous · Answer

Start by raising each side by 2

anonymous · Answer

So, 2^(log2(2x+5)<2^0

anonymous · Answer

Then you get 2x+5<2^0

You get 2x+5<1

2x<-5+1

2x<-4....

Divide both sides by 2

You eventually get x<-2

anonymous · Answer

the answer is -5/2<x<-2.

anonymous · Answer

according to my textbook

anonymous · Answer

Yes, that is correct, I only solved for 1 side.

anonymous · Answer

how do you solve for the other side?

lgbasallote · Answer

still need help?

anonymous · Answer

yes

anonymous · Answer

@lgbasallote

lgbasallote · Answer

try substituting -5/2 into x in $$\log_2 (2x + 5)$$maybe that will help you figure out why x > -5/2

anonymous · Answer

I know that $$\log_{2}0  $$does not exist but how would you find that algebraically

lgbasallote · Answer

ah. you are so close. log_a (0) does "exist"...however it's value is -$\infty$

lgbasallote · Answer

well that is if 0 is approaching from the right....but that's calculus stuff....

lgbasallote · Answer

the point is... x > -5/2 because -5/2 is the value of x that will make the logarithm equal to -infinity...and as you know, you're looking for the value of x that will make the logarithm negative. So, your range of values will be from the first number that will make it negative (which is -2) until the number which will make it become -infinity..does that make sense?

anonymous · Answer

then why can't we include -5/2, -infinity is less than 0 and therefore part of the solution

lgbasallote · Answer

because -infinity is not a real number

anonymous · Answer

and also to find -5/2, would you just have solve for what makes (2x+5)= 0

anonymous · Answer

is it implied that a solution set is only real numbers

lgbasallote · Answer

exactly

lgbasallote · Answer

that's why you don't include infinity

lgbasallote · Answer

because infinity is not real

lgbasallote · Answer

...would you like a more detailed explanation?

lgbasallote · Answer

it might help you understand better....or it might confuse you more...your choice...

anonymous · Answer

no I understand
and about finding -5/2, would I just have to look for the number that makes (2x+5) = 0?

lgbasallote · Answer

no. you look for 2x + 5 > 0

anonymous · Answer

well I mean the other limit of the solution set. not -2

lgbasallote · Answer

yes. you solve x > -5/2 by doing 2x + 5 > 0

anonymous · Answer

okay go it
thanks for your help

lgbasallote · Answer

welcome