What is ln(10)(x^{1/3}y^{1/3}z^{1/3}) 1/x ?

The solution to ln(10)(x^{1/3}y^{1/3}z^{1/3}) 1/x is (ln(10)y^{1/3}z^{1/3})/(x^{2/3)}

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simplify ln(10)(x^{1/3}y^{1/3}z^{1/3}) 1/x

simplify

ln (10) (x^{\frac{1}{3}} y^{\frac{1}{3}} z^{\frac{1}{3}}) \frac{1}{x}

\frac{ln ( 10 ) y ^{\frac{1}{3}} z ^{\frac{1}{3}}}{x ^{\frac{2}{3}}}

Solution steps

ln (10) (x^{\frac{1}{3}} y^{\frac{1}{3}} z^{\frac{1}{3}}) \frac{1}{x}

Apply exponent rule:

a^{m} b^{m} = (ab)^{m},

assuming

a \geq 0, b \geq 0

x^{\frac{1}{3}} y^{\frac{1}{3}} z^{\frac{1}{3}} = (x yz)^{\frac{1}{3}}

= ln (10) \frac{1}{x} (x yz)^{\frac{1}{3}}

Multiply fractions:

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

= \frac{1 \cdot ln ( 10 ) ( x yz ) ^{\frac{1}{3}}}{x}

Multiply:

1 \cdot ln (10) = ln (10)

= \frac{ln ( 10 ) ( x yz ) ^{\frac{1}{3}}}{x}

Factor

(x yz)^{\frac{1}{3}} : x^{\frac{1}{3}} y^{\frac{1}{3}} z^{\frac{1}{3}}

= \frac{ln ( 10 ) x ^{\frac{1}{3}} y ^{\frac{1}{3}} z ^{\frac{1}{3}}}{x}

Cancel

\frac{ln ( 10 ) x ^{\frac{1}{3}} y ^{\frac{1}{3}} z ^{\frac{1}{3}}}{x} : \frac{ln ( 10 ) y ^{\frac{1}{3}} z ^{\frac{1}{3}}}{x ^{\frac{2}{3}}}

= \frac{ln ( 10 ) y ^{\frac{1}{3}} z ^{\frac{1}{3}}}{x ^{\frac{2}{3}}}

680 e^{- 0.0892 (5)} \cdot (- 0.0892)

4 + 7 \cdot 4 - 7

^{'} 1 0^{- 3} 1 0^{- 5}

(f \circ f^{- 1}) (10)

What is ln(10)(x^{1/3}y^{1/3}z^{1/3}) 1/x ?
The solution to ln(10)(x^{1/3}y^{1/3}z^{1/3}) 1/x is (ln(10)y^{1/3}z^{1/3})/(x^{2/3)}