What is ln(x^3)-5ln(\sqrt[5]{x^2}) ?

The solution to ln(x^3)-5ln(\sqrt[5]{x^2}) is ln(x)

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simplify ln(x^3)-5ln(\sqrt[5]{x^2})

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)

ln (\frac{x}{x + 1})

lo g_{2} (x) + lo g_{2} (10) - 5 lo g_{2} (x)

lo g_{b} (24) - lo g_{b} (8)

lo g_{10} (4) - lo g_{10} (24)

f (x) = lo g_{10} (3 x + 9) + lo g_{10} (x + 8)

What is ln(x^3)-5ln(\sqrt[5]{x^2}) ?
The solution to ln(x^3)-5ln(\sqrt[5]{x^2}) is ln(x)