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Popular >

simplify ln(1/(\sqrt[3]{e^2)})

Solution

simplify

Solution

- \frac{2}{3}

+1

Decimal Notation

- 0.66666 \dots

Solution steps

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

Rewrite as

= - ln ((e^{2})^{\frac{1}{3}})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= - \frac{1}{3} ln (e^{2})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= - 2 \cdot \frac{1}{3} ln (e)

Apply log rule:

lo g_{a} (a) = 1

= - 2 \cdot \frac{1}{3}

Simplify

= - \frac{2}{3}

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Frequently Asked Questions (FAQ)

What is ln(1/(\sqrt[3]{e^2)}) ?
The solution to ln(1/(\sqrt[3]{e^2)}) is -2/3