化简 4^{log_{2}(5)+2log_{0.25}(3)}

解答

化简

4^{l o g_{2} (5) + 2 l o g_{0.25} (3)}

2.77777 \dots

求解步骤

4^{l o g_{2} (5) + 2 l o g_{0.25} (3)}

使用指数法则:

a^{b + c} = a^{b} a^{c}

= 4^{l o g_{2} (5)} \cdot 4^{2 l o g_{0.25} (3)}

化简

4^{l o g_{2} (5)} : 5^{2}

= 5^{2} \cdot 4^{2 l o g_{0.25} (3)}

5^{2} = 25

= 25 \cdot 4^{2 l o g_{0.25} (3)}

4^{2 l o g_{0.25} (3)} = 0.11111 \dots

= 25 \cdot 0.11111 \dots

数字相乘:

25 \cdot 0.11111 \dots = 2.77777 \dots

= 2.77777 \dots

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