How Do You Solve Logarithmic Expressions Involving Fractions?

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To solve log_2(15/2) using the given values log_2(5) = x and log_2(3) = y, first apply the logarithmic property that states log_b(a/c) = log_b(a) - log_b(c). This leads to log_2(15) - log_2(2), where log_2(15) can be expressed as log_2(3*5) = log_2(3) + log_2(5) = y + x. Since log_2(2) equals 1, the expression simplifies to (x + y) - 1. Thus, log_2(15/2) can be expressed as x + y - 1, confirming that the correct answer is option D.
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If log_2 (5) = x and log_2 (3) = y , determine an expression for log_2 (15/2), in terms of x and y.
A. xy
B. x + y
C. xy - 1
D. x + y - 1

I'm suppose to solve this by hand but it doesn't seem possible. I tried so many ways but the does not come out as D. which is the answer Can someone explain the steps to this problem? Thanks!
 
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Hint: log2(15/2) = log2(15) - log2(2)
 

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