The question gives a logarithmic relationship (e.g., log_a b = k) and asks the student to express a different logarithmic quantity in terms of the given variable(s) using change-of-base and algebraic manipulation.
$$\log_{3} 5 = a$$ Given this, what is the value of $\log_{5} 15$? A) $\frac{a}{a+1}$ B) $\frac{a+1}{a}$ C) $\frac{a}{a+3}$ D) $\frac{a+3}{a}$ E) $\frac{4a}{3}$
For real numbers x and y $$2 ^ { x } = 6 ^ { x + y - 1 }$$ Given this, what is $3 ^ { \mathbf { x } }$ in terms of y? A) $3 ^ { 1 - y }$ B) $6 ^ { 1 - y }$ C) $6 ^ { y }$ D) $9 ^ { - y }$ E) $9 ^ { 1 + y }$