I think we should show When field $F$ is Quotient field , $\log_{10} 7$ is transcendental in $F(\log_{10} 2,\log_{10} 3)$. But I don't know how to do...
How to prove $\log_{10} 7$ is cannot be exactly calculated by $\log_{10} 2$ & $\log_{10} 3$
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abstract-algebra
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0What is meant by "exactly calculated by"? – 2017-02-06
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0@user254665 That is made precise in the question by the term "transcendental" – 2017-02-06
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0Perhaps you should specify what $F$ is the quotient field of. – 2017-02-07
1 Answers
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Hint: $7$ can't be expressed as $2^{a}.3^{b}$. Where $ a, b$ are rational numbers.