Algebra
Logarithmic system of equations
MJAT_TS7_P1
Grade 12
Question:
Let $a=3^{2/3}$ and $b=5^{1/6}\cdot\dfrac{1}{6}$. If $x,y\in\mathbb{R}$ satisfy $5^{3x+2y}=\log_a 18^4$ and $2x-y=\log_b(1080)$, then $4x+5y$ equals:
Step-by-Step Solution
Key Concept: Compute $\log_a 18^4$ with $a=3^{2/3}$: $\log_{3^{2/3}}18^4=\frac{4\log_3 18}{2/3}=6\log_3 18$. Similarly compute $\log_b(1080)$. Solve the system for $x,y$.
$4x+5y=\mathbf{8}$.
Correct Answer: 8