Problem of the Day

If \displaystyle 0.375^3=2^a3^b6^c, what is the value of \displaystyle b-a?

A. 2
B. 3
C. 6
D. 12
E. 18

Reveal Answer


D. 12

See the Solution



The key to this problem is to recognize that $0.375=\frac{3}{8}$. Then you can proceed in the following manner:


$\displaystyle (\frac{3}{8})^3=2^a3^b6^c$

$\displaystyle \frac{3^3}{8^3}=2^a3^b6^c$


$3^3(2^3)^{-3}=2^a3^b(2\cdot 3)^c$



$a+c=-9$ and $b+c=3$

$(b+c)-(a+c)=3- -9$



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