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If \(\frac{2.25\cdot10^a}{0.15\cdot10^b}=1.5\cdot10^3,\)

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by M7MBA » Tue Apr 30, 2019 1:11 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

If \(\frac{2.25\cdot10^a}{0.15\cdot10^b}=1.5\cdot10^3,\) then \(a - b =\)

A. 1
B. 2
C. 3
D. 4
E. 5

[spoiler]OA=B[/spoiler]

Source: Princeton Review
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by Jay@ManhattanReview » Tue Apr 30, 2019 8:30 pm
M7MBA wrote:If \(\frac{2.25\cdot10^a}{0.15\cdot10^b}=1.5\cdot10^3,\) then \(a - b =\)

A. 1
B. 2
C. 3
D. 4
E. 5

[spoiler]OA=B[/spoiler]

Source: Princeton Review
We have

\(\frac{2.25\cdot10^a}{0.15\cdot10^b}=1.5\cdot10^3,\)

\(\frac{225\cdot10^a}{15\cdot10^b}=1.5\cdot10^3,\)

\((15\cdot10^{(a - b)})=1.5\cdot10^3,\)

\((1.5\cdot10\cdot10^{(a - b)})=1.5\cdot10^3,\)

\((10^{(a - b + 1)})=10^3,\)

=> a - b + 1 = 3

a - b = 2

The correct answer: B

Hope this helps!

-Jay
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