Question

芽瑠

この問題教えてください

a+b
a>0, b>0 のとき, 不等式10g10-
2
成り立つときを調べよ。
log104 +10g106 を証明せよ。また,等号が
2

Answer 1

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右辺を式変形しましょう

Answer 2

Dw

That is a Strictly Increasing Function and a special case of Jensen's inequality for convex functions. The logarithm function is concave, and Jensen's inequality tells us that for a concave function, the function's value at the average point is greater than or equal to the average of the function's values.

On the contrary, if we consider the situation with a convex function, the value of the function at the average point will be less than or equal to the average of the function’s values.