Thriving Scholars TMUA Full Mock Test 1 Paper 1 · Question 11

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Thriving Scholars TMUA Full Mock Test 1 Paper 1 · Q11

Paper 1Sequences & seriesPowers & logarithmsNumber & counting

Define binary operations $\diamond$ and $\heartsuit$ by

a\diamond b=a^{\log_7(b)}\qquad\text{and}\qquad a\heartsuit b=a^{1/\log_7(b)}

for all real numbers $a$ and $b$ for which these expressions are defined. The sequence $(a_n)$ is defined recursively by $a_3=3\heartsuit2$ and

a_n=(n\heartsuit(n-1))\diamond a_{n-1}

for all integers $n\ge4$ . To the nearest integer, what is $\log_7(a_{2019})$ ?

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