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Oliver
10-26-2013, 05:38 AM
If 4^a \cdot 4^b =7^{2c}, which one of the following is the value of \frac{a+b}{2c}?


(A) \frac{log7}{log4}

(B) \frac{log4}{ log7}

(C) log4 \cdot log7

(D) log(4 \cdot 7)

Thanks!

nicole
10-26-2013, 05:38 AM
Using properties of exponents and logarithms we have the following

4^a \cdot 4^b =7^{2c} \Rightarrow 4^{a+b}=7^{2c} \Rightarrow

log(4^{a+b})=log(7^{2c})\Rightarrow (a+b)log4=(2c)log7 \Rightarrow

\frac{a+b }{2c} =\frac{log7}{log4}


Therefore the correct answer is (A).:)

Oliver
10-26-2013, 05:39 AM
Thanks Nicole!