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If (500)(7,000) = (350)(100^x)

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If (500)(7,000) = (350)(100^x)  [#permalink]

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New post 22 Dec 2014, 07:29
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If (500)(7,000) = (350)(100^x), what is the value of x?

(A)5

(B)4

(C)3

(D)2

(E)1

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Re: If (500)(7,000) = (350)(100^x)  [#permalink]

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New post 22 Dec 2014, 10:38
(500)(7,000) = (350)(100^x)
=> (500)(7,000)/350 = 100^x
=> 10,000 = 100^x
=> 100^2 = 100^x
Since, base is same so powers will be same too.
So, x=2
Answer will be D

Hope it helps!
uday1409 wrote:
If (500)(7,000) = (350)(100^x), what is the value of x?

(A)5

(B)4

(C)3

(D)2

(E)1

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Re: If (500)(7,000) = (350)(100^x)  [#permalink]

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New post 22 Dec 2014, 14:59
Hi uday1409,

When multiplying numbers that end in 0, there's a great "math shortcut" that you can use:

Here, we're told...

(500)(7000) = 350(100^X) and we're asked for the value of X...

Let's start with the "left side" of the equation:
(5)(7) = 35

There are two 0s in the first parentheses) and three 0s in the second parentheses, so we'll have FIVE 0s in total (following the 35):

3,500,000

On the "right side" of the equation:

We have 350, which is 35 with one 0. We need FOUR MORE 0s for the equation to equal...

(100) has two 0s
(100^2) = (100)(100) has four 0s

So, X MUST = 2....

(350)(100)(100) =

3,500,000

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Re: If (500)(7,000) = (350)(100^x)  [#permalink]

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New post 22 Dec 2014, 18:52
(500)(7,000) = (350)(100^x)
5*7*10^5=5*7*10*10^2x
5*7*10^5=5*7*10^(2x+1)
5=2x+1
x=2
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Re: If (500)(7,000) = (350)(100^x)  [#permalink]

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New post 23 Dec 2014, 05:26
(500*7000)=350*100^x ==> 35 00000 = 350 100^x (we need to equal the number of "0" on both sides. Hence 100^x should have four "0" ==> 100^x = 10 000 ==> x=2). Hope it is clear
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Re: If (500)(7,000) = (350)(100^x)  [#permalink]

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New post 08 Aug 2018, 07:28
uday1409 wrote:
If (500)(7,000) = (350)(100^x), what is the value of x?

(A)5

(B)4

(C)3

(D)2

(E)1

\((500)(7,000) = (350)(100^x)\)

Or, \((3500000) = (350)(100^x)\)

Or, \(10000 = 100^x\)

Thus, x = 2, Answer must be (D)
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If (500)(7,000) = (350)(100^x)  [#permalink]

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New post 08 Aug 2018, 09:32
uday1409 wrote:
If (500)(7,000) = (350)(100^x), what is the value of x?

(A)5

(B)4

(C)3

(D)2

(E)1

Separate 35 and powers of 10 on both sides
\((5*10^2)(7*10^3)=(35*10^1)(100^{x})\)

\((5*7)(10^2*10^3)=(35)(10^1)*(10^2)^{x})\)

\((35)(10^{(2+3)})=(35)(10^1)(10^{(2*x)})\)

\((35)(10^5)=(35)(10^{(1+2x)})\)


Factor out 35 (i.e., use only the bases with exponents)
\(10^5=10^{(1+2x)}\)
Bases are equal. Set the exponents equal
\(5=(1+2x)\)
\(2x=4\)
\(x=2\)

Answer B
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If (500)(7,000) = (350)(100^x)   [#permalink] 08 Aug 2018, 09:32
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