What is ln(x^5)-3ln(\sqrt[3]{x^4}) ?

The solution to ln(x^5)-3ln(\sqrt[3]{x^4}) is ln(x)

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simplify ln(x^5)-3ln(\sqrt[3]{x^4})

simplify

ln (x)

Solution steps

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

Simplify

= ln (x)

lo g_{10} (3 \cdot 2^{3})

\frac{1}{2} lo g_{c} (x) + 4 lo g_{c} (y) - 3 lo g_{c} (x)

ln (12 x)

lo g_{b} (9) + 3 lo g_{b} (2)

\frac{1}{4} lo g_{c} (x) + 3 lo g_{c} (y) - 2 lo g_{c} (x)

What is ln(x^5)-3ln(\sqrt[3]{x^4}) ?
The solution to ln(x^5)-3ln(\sqrt[3]{x^4}) is ln(x)