csat-suneung 2024 Q9

csat-suneung · South-Korea · csat__math 4 marks Laws of Logarithms Simplify or Evaluate a Logarithmic Expression

For two points $\mathrm{P}(\log_5 3)$ and $\mathrm{Q}(\log_5 12)$ on a number line, the point that divides the line segment PQ internally in the ratio $m:(1-m)$ has coordinate 1. Find the value of $4^m$. (Here, $m$ is a constant with $0 < m < 1$.) [4 points]
(1) $\frac{7}{6}$
(2) $\frac{4}{3}$
(3) $\frac{3}{2}$
(4) $\frac{5}{3}$
(5) $\frac{11}{6}$

For two points $\mathrm{P}(\log_5 3)$ and $\mathrm{Q}(\log_5 12)$ on a number line, the point that divides the line segment PQ internally in the ratio $m:(1-m)$ has coordinate 1. Find the value of $4^m$. (Here, $m$ is a constant with $0 < m < 1$.) [4 points]\\
(1) $\frac{7}{6}$\\
(2) $\frac{4}{3}$\\
(3) $\frac{3}{2}$\\
(4) $\frac{5}{3}$\\
(5) $\frac{11}{6}$

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q23_calculus Q23_geometry Q24 Q24_calculus Q24_geometry Q25 Q25_calculus Q25_geometry Q26 Q26_calculus Q26_geometry Q27 Q27_calculus Q27_geometry Q28 Q28_calculus Q28_geometry Q29 Q29_geometry Q30 Q30_geometry