turkey-yks 2025 Q17

turkey-yks · Other · yks-ayt Laws of Logarithms Solve a Logarithmic Equation
Let $a$ and $b$ be non-consecutive positive integers. The equality
$$\ln(a!) = \ln(b!) + 3 \cdot \ln 2 + 2 \cdot \ln 3 + \ln 7$$
is satisfied. Accordingly, what is the sum $a + b$?
A) 10 B) 13 C) 15 D) 18 E) 20
Let $a$ and $b$ be non-consecutive positive integers. The equality

$$\ln(a!) = \ln(b!) + 3 \cdot \ln 2 + 2 \cdot \ln 3 + \ln 7$$

is satisfied.
Accordingly, what is the sum $a + b$?

A) 10
B) 13
C) 15
D) 18
E) 20