If (4000)(6,000) = (240)(100expo(x)), what is the value of x ?

20*200*30*200=240*100^(x)

20*200*30*200=12*20*100^(x)

20*200*30*200/12*20=100^(x)

200*30*200/12=100^(x)

100*5*200=100^(x)

10^2*10^3=100^(x)

10^(5)=10^(2x)
x=5/2

Xbond wrote:Hi there,

Could you explain the concept of this DS in simplest way

If (4000)(6,000) = (240)(100expo(x)), what is the value of x ?

a)5
b)4
c)3
d)2
e)1

We see that the left side and the right side look dissimilar; to simplify the question, let's make them look the same.

Our first hint on how to proceed is the "4" and the "6" on the left side of the equation, which we know will give us 24. Accordingly, let's multiply out the left side:

4000 * 6000 = 24000000

We want a 240 on the left side, so let's rewrite 24000000 as 240*100000.

Accordingly, we have:

240 * 100000 = 240 * 100^x

Dividing each side by 240, we get:

100000 = 100^x

Sadly, the left side has an odd number of "0"s, so things aren't going to work out perfectly. We want to put the left side with base 100, so we can rewrite it as:

100 * 100 * 10.

Well, 100 * 100 would make x=2; 100*100*100 would make x=3; we want an answer in between, which should be good enough to pick the right answer on a multiple choice test.

Sadly, the right answer doesn't appear amongst the choices you've listed, leaving three possibilities:

1) you mistyped the question;
2) you mistyped the choices; and
3) the question is erroneous.

(If the right side were supposed to be 10^x instead of 100^x, the answer would be (A).)

Many thks, I will check

Xbond wrote:Hi there,

Could you explain the concept of this DS in simplest way

If (4000)(6,000) = (240)(100expo(x)), what is the value of x ?

a)5
b)4
c)3
d)2
e)1

is OA C?