What is log_{5}(\sqrt[3]{x^2+1}) ?

The solution to log_{5}(\sqrt[3]{x^2+1}) is 1/3 log_{5}(x^2+1)

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simplify log_{5}(\sqrt[3]{x^2+1})

simplify

\frac{1}{3} lo g_{5} (x^{2} + 1)

Solution steps

Rewrite as

= lo g_{5} ((x^{2} + 1)^{\frac{1}{3}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{3} lo g_{5} (x^{2} + 1)

0.2 \times 100

(- 10)^{4}

(x - \frac{1}{2}) (x - \frac{1}{2})

\frac{12}{90}

\frac{\frac{7}{2}}{2}

What is log_{5}(\sqrt[3]{x^2+1}) ?
The solution to log_{5}(\sqrt[3]{x^2+1}) is 1/3 log_{5}(x^2+1)