1. ## Solve Logarithm Inequality

Hi--I have the following problem:

Solve the inequality log2(112)is less than x. (2 is the base)
I did this problem and got x is less than 4. However, I was told this is the incorrect answer. It should be x is more than 4. I thought that you only had a change in the equality sign when you are multiplying or dividing by a negative number. Why did this inequality sign change direction?

Thanks for explaining it to me.

Joanie

2. Hello, Joanie!

If no one is responding, it's that we don't understand the problem.
And the answers (yours and theirs) are baffling.

Could you give us the original wording?

Solve the inequality: .$\displaystyle \log_2(112)\: < \:x$ . ??
It says: .$\displaystyle x \:> \:\log_2(112)$ . . . It's already solved!

By the way, that's how they "changed the sign" .

If we have: .$\displaystyle 2 < 7$ .("Two is less than seven")
. . we can write: .$\displaystyle 7 > 2$ .("Seven is greater than two")

We didn't "change the sign", we reversed the entire statement.

"John is taller than Mary" .= ."Mary is shorter than John." . . . . Get it?

I did this problem and got: .$\displaystyle x < 4$ . ??
How did you do that?

However, I was told it should be: .$\displaystyle x > 4$ . ??
How did they do that?

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Is a puzzlement!

It turns out that: $\displaystyle \log_2(112) \:\approx\:6.81$

So they gave us: .$\displaystyle x \:>\:6.81$

And they ask us to "solve for $\displaystyle x$" . . . Rather silly, isn't it?

Then they shout, "You're wrong! .The answer is: $\displaystyle x > 4$"

Someone has been taking too much cough syrup . . .

3. Originally Posted by Joanie
Hi--I have the following problem:

Solve the inequality log2(112)is less than x. (2 is the base)
$\displaystyle \log_2112<x?$ There is nothing here to solve.

I did this problem and got x is less than 4. However, I was told this is the incorrect answer. It should be x is more than 4.
Assuming you gave the correct inequality, $\displaystyle x>4$ does not work. For example, $\displaystyle 2^5=32<112,$ so $\displaystyle x=5$ does not satisfy the inequality. $\displaystyle x<4$ similarly does not work.