If $$ a, b $$ and $$ c $$ are positive real numbers such that $$ a 10 \geq b \geq c $$ and

$$
\frac{\log_8 (a + b)}{\log_2 c} + \frac{\log_{27} (a - b)}{\log_3 c} = \frac{2}{3}
$$

then the greatest possible integer value of $$ a $$ is

Question

If $$ a, b $$ and $$ c $$ are positive real numbers such that $$ a > 10 \geq b \geq c $$ and

$$
\frac{\log_8 (a + b)}{\log_2 c} + \frac{\log_{27} (a - b)}{\log_3 c} = \frac{2}{3}
$$

then the greatest possible integer value of $$ a $$ is

Accepted Answer

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1748584387/aptidude_questions/vmwhbrbfrirwmtipqcd8.png)