7. For what value of p does 12^{2p1} = 5(3.7)^{p} ?
A. (ln 5  ln 12)/(ln 3.7  ln 12) 
B. (ln 5 + ln 12)/(2 ln 12  ln 3.7) 
C. (ln 12)/(2 ln 12 – 5 ln 3.7) 
D (ln 12)/(ln 12 – 5 ln 3.7). 
E. (ln 12  ln 5)/(2 ln 12 + ln 3.7) 

Solution: The answer is B
Using the properties of logarithms solve for p as follows:
Given,
Take the natural logarithm of both sides of the above equation,
Since, ln (uv) = ln u + ln v and ln u^{n} = n ln u, the above equation can be rewritten as follows,
Solving for p yields,