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受欢迎的代数 >

50 1/3 =\sqrt[n]{50}

解答

50 \frac{1}{3} = n 50

解答

n = \frac{ln ( 50 )}{ln ( \frac{151}{3} )}

+1

十进制

n = 0.99830 \dots

求解步骤

50 \frac{1}{3} = n 50

将带分数转换为假分式:

50 \frac{1}{3} = \frac{151}{3}

\frac{151}{3} = n 50

在两边乘以

3

\frac{151}{3} \cdot 3 = n 50 \cdot 3

化简

151 = n 50 \cdot 3

交换两边

n 50 \cdot 3 = 151

两边除以

3

n 50 = \frac{151}{3}

使用指数运算法则

\frac{1}{n} ln (50) = ln (\frac{151}{3})

解

\frac{1}{n} ln (50) = ln (\frac{151}{3}) : n = \frac{ln ( 50 )}{ln ( \frac{151}{3} )}

n = \frac{ln ( 50 )}{ln ( \frac{151}{3} )}

验证解:

n = \frac{ln ( 50 )}{ln ( \frac{151}{3} )}

真

解是

n = \frac{ln ( 50 )}{ln ( \frac{151}{3} )}

作图

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