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Omni-MATH / Let a and b be real numbers greater than 1 such that ab=100. The maximum possible value of a^((log₁₀b)²) can be written in the form 10^(x) for some real number x. Find x.

Problem

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problem

Let aa and bb be real numbers greater than 1 such that ab=100a b=100. The maximum possible value of a(log10b)2a^{(\log_{10} b)^{2}} can be written in the form 10x10^{x} for some real number xx. Find xx.
Plain-text mathematical notation (without MathML)
Let a and b be real numbers greater than 1 such that ab=100. The maximum possible value of a^((log₁₀b)²) can be written in the form 10^(x) for some real number x. Find x.
Original LaTeX notation
Let $a$ and $b$ be real numbers greater than 1 such that $a b=100$. The maximum possible value of $a^{(\log_{10} b)^{2}}$ can be written in the form $10^{x}$ for some real number $x$. Find $x$.

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Source and history

task_id
0d5394dc-60d7-53d2-86a8-05dba8ca001b
task_key
test--0d5394dc-60d7-53d2-86a8-05dba8ca001b
task_revision_id
1
config / split
/ test

Official source

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