sinh(log_{10}(2)-log_{10}(5))

解

sinh (lo g_{10} (2) - lo g_{10} (5))

\frac{e ^{l o g_{10} (2) - l o g_{10} (5)} - e ^{- l o g_{10} (2) + l o g_{10} (5)}}{2}

十進法表記

- 0.40852 \dots

解答ステップ

sinh (lo g_{10} (2) - lo g_{10} (5))

双曲線の公式を使用する:

sinh (x) = \frac{e ^{x} - e ^{- x}}{2}

= \frac{e ^{l o g_{10} (2) - l o g_{10} (5)} - e ^{- (l o g_{10} (2) - l o g_{10} (5))}}{2}

簡素化

= \frac{e ^{l o g_{10} (2) - l o g_{10} (5)} - e ^{- l o g_{10} (2) + l o g_{10} (5)}}{2}