SajjadAhmad wrote:

\(\frac{0.0027x10^x}{0.09x10^y}\)=3x10^8 What is the value of y less than x?

A 9

B 10

C 11

D 12

E 13

In stages\(\frac{0.0027*10^x}{0.09*10^y}\)=\(3*10^8\) REWRITE

\(\frac{27*10^{-4}*10{^x}}{9*10^{-2}*10{^y}}\) =\(3*10^8\)

Switch the negative powers of 10:

\(\frac{27*10^{2}*10^{x}}{9*10^{4}*10^{y}}\) =\(3*10^8\)

DIVIDE:

\(3*10^{(2-4)}*10^{(x-y)} = 3*10^8\)

Factor out 3

\(10^{(2-4)}*10^{(x-y)} = 10^8\)

Divide by

\(10^{-2}\)\(\frac{10^{-2}*10^{(x-y)}}{10^{-2}} = \frac{10^8}{10^{-2}}\)

Simplify:

\(10^{(x-y)} = 10^{(8- (-2))}\)

\(10^{(x-y)} = 10^{10}\)

"

y less than x" means "\(x - y\)"

Bases are identical, set the exponents equal. The value of y less than x is

\(x - y = 10\)

ANSWER B

In fewer steps\(\frac{0.0027*10^x}{0.09*10^y}\)=\(3*10^8\)

\((.03)*10^{x-y} = 3 * 10^8\)

\(3*10^{-2}*10^{x-y} = 3 * 10^8\)

\(10^{x-y} = 10^{10}\)

\(x - y = 10\)

ANSWER B

SajjadAhmad , thank you for the question. I had a hard time differentiating between what I thought was variable \(x\), and "x" as multiplication. I think it might be better to use an asterisk, as I did. JMO.

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