turkey-yks 2024 Q13

turkey-yks · Other · yks-ayt Laws of Logarithms Solve a Logarithmic Equation
Let $a$, $x$ and $y$ be positive real numbers. The numbers
$$\log_{a} x, \quad \log_{a} y, \quad \log_{a}(x+y)$$
arranged from smallest to largest are consecutive integers. What is the value of $\log_{a}(2a+1)$?
A) $-2$ B) $-1$ C) $2$ D) $3$ E) $4$
Let $a$, $x$ and $y$ be positive real numbers. The numbers

$$\log_{a} x, \quad \log_{a} y, \quad \log_{a}(x+y)$$

arranged from smallest to largest are consecutive integers. What is the value of $\log_{a}(2a+1)$?

A) $-2$
B) $-1$
C) $2$
D) $3$
E) $4$