# What does this mean: x^(+42)?

1. Aug 5, 2011

### ArcanaNoir

1. The problem statement, all variables and given/known data

I was doing some GRE practice problems, and I got this question:
$$(2^4x)(4^3x)=8x^{+42}$$

3. The attempt at a solution

At first I thought it was a typo or something, but the detailed answer given did some weird stuff and in the end, $x=18$

What is this?? The only time I've seen a + in the exponent is in addition, as in $x^{1+t}$ or when talking about a limit approaching from the left or the right. So... can anyone clue me in?

2. Aug 5, 2011

### BloodyFrozen

What was the detailed answer?

3. Aug 5, 2011

4. Aug 5, 2011

### I like Serena

Hi ArcanaNoir!

This looks like one big typo.
Looking at the explanation, I think the intended equation was:
$$(2^{4x})(4^{3x})=8^{x+42}$$
Note that in the explanation there is yet another typo when they say +24 when obviously +42 was meant.
Seems to me the author used LaTeX, but was as yet apparently not aware that he should use curly braces in exponents.
To compensate, curvy thingies were added.

5. Aug 5, 2011

### ArcanaNoir

Oh thank goodness. I thought this was some new math I didn't know. I worked it out according to your correction and I got it just fine. Thanks a million!

6. Aug 7, 2011

### Staff: Mentor

In case there are others as perplexed as I have been, let's examine the original maths question.

Skip over all the preceding, and the problem you face is finding the value of x which makes I like Serena's equation above true.

The LHS can be rewritten as: 24x.(22)3x

and using exponent properties this simplifies to: 210x

The RHS can be rewritten as: (23)(x+42)

and simplified to: 23(x+42)

Now, having equal bases on each side, we can equate the powers,
giving: 10x = 3x + 126

And solving for x, we have the solution: x=18

It's a hard task where working out the correct question is at least as difficult as working out the correct answer!

Last edited: Aug 7, 2011