If a , b a, b a , b and c c c are positive real numbers such that a > 10 ≥ b ≥ c a > 10 \geq b \geq c a > 10 ≥ b ≥ c and log ⁡ 8 ( a + b ) lo...

CAT Hard Logarithms Integer

Question

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

Enter your answer as an integer value

cat 2024logarithmic equationsinteger solutions

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