csat-suneung 2009 Q19

csat-suneung · South-Korea · csat__math-humanities 3 marks Laws of Logarithms Solve a Logarithmic Equation
For two real numbers $a , b$ with $1 < a < b$,
$$\frac { 3 a } { \log _ { a } b } = \frac { b } { 2 \log _ { b } a } = \frac { 3 a + b } { 3 }$$
holds. Find the value of $10 \log _ { a } b$. [3 points]
For two real numbers $a , b$ with $1 < a < b$,

$$\frac { 3 a } { \log _ { a } b } = \frac { b } { 2 \log _ { b } a } = \frac { 3 a + b } { 3 }$$

holds. Find the value of $10 \log _ { a } b$. [3 points]