Thriving Scholars TMUA Full Mock Test 1 Paper 2 · Question 17

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Thriving Scholars TMUA Full Mock Test 1 Paper 2 · Q17

Paper 2Powers & logarithms

Positive real numbers $a$ and $b$ have the property that

\sqrt{\log a}+\sqrt{\log b}+\log\sqrt a+\log\sqrt b=100

and all four terms on the left are positive integers, where $\log$ denotes the base 10 logarithm. What is $ab$ ?

10^{52}

10^{100}

10^{144}

10^{164}

10^{200}

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