化简 (ln(c^{-4}))(ln(a/(b^2)))^{-4}

解答

化简

(ln (c^{- 4})) (ln (\frac{a}{b ^{2}}))^{- 4}

- \frac{4 ln ( c )}{( ln ( a ) - 2 ln ( b ) ) ^{4}}

求解步骤

(ln (c^{- 4})) (ln (\frac{a}{b ^{2}}))^{- 4}

使用指数法则:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{( ln ( \frac{a}{b ^{2}} ) ) ^{4}} ln (c^{- 4})

化简

ln (c^{- 4}) : - 4 ln (c)

= - 4 \cdot \frac{1}{ln ^{4} ( \frac{a}{b ^{2}} )} ln (c)

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{1 \cdot 4 ln ( c )}{ln ^{4} ( \frac{a}{b ^{2}} )}

数字相乘:

1 \cdot 4 = 4

= - \frac{4 ln ( c )}{ln ^{4} ( \frac{a}{b ^{2}} )}

ln^{4} (\frac{a}{b ^{2}}) = (ln (a) - 2 ln (b))^{4}

= - \frac{4 ln ( c )}{( ln ( a ) - 2 ln ( b ) ) ^{4}}

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