簡約 16^{log_{2}(3)}

解

簡約

1 6^{l o g_{2} (3)}

81

解答ステップ

1 6^{l o g_{2} (3)}

数を因数に分解する:

16 = 2^{4}

= (2^{4})^{l o g_{2} (3)}

指数の規則を適用する:

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

= 2^{4 l o g_{2} (3)}

指数の規則を適用する:

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

2^{4 l o g_{2} (3)} = (2^{l o g_{2} (3)})^{4}

= (2^{l o g_{2} (3)})^{4}

対数の規則を適用する:

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

2^{l o g_{2} (3)} = 3

= 3^{4}

3^{4} = 81

= 81