簡約 100^{log_{10}(x)}

解

簡約

10 0^{l o g_{10} (x)}

x^{2}

解答ステップ

10 0^{l o g_{10} (x)}

数を因数に分解する:

100 = 1 0^{2}

= (1 0^{2})^{l o g_{10} (x)}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}, a \geq 0

= 1 0^{2 l o g_{10} (x)}

指数の規則を適用する:

a^{b c} = (a^{b})^{c}, a \geq 0

1 0^{2 l o g_{10} (x)} = (1 0^{l o g_{10} (x)})^{2}

= (1 0^{l o g_{10} (x)})^{2}

対数の規則を適用する:

a^{l o g_{a} (b)} = b

1 0^{l o g_{10} (x)} = x

= x^{2}