What is the solution for x in the equation (2^4x)(4^3x)=8x^(+42)?

[ArcanaNoir]

Homework Statement

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

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?

 

[BloodyFrozen]

Homework Statement

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

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, [itex] x=18 [/itex]

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?

What was the detailed answer?

 

[ArcanaNoir]

 

[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.

 

[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!

 

[NascentOxygen]

the intended equation was:
$$(2^{4x})(4^{3x})=8^{x+42}$$

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: 2^4x.(2²)^3x

and using exponent properties this simplifies to: 2^10x

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

and simplified to: 2^3(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!