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Popular >

simplify ln(x^3)-5ln(x)

Solution

simplify

ln (x^{3}) - 5 ln (x)

Solution

- ln (x^{2})

Solution steps

ln (x^{3}) - 5 ln (x)

Apply log rule:

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

5 ln (x) = ln (x^{5})

= ln (x^{3}) - ln (x^{5})

Apply log rule:

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

ln (x^{3}) - ln (x^{5}) = ln (\frac{x ^{3}}{x ^{5}})

= ln (\frac{x ^{3}}{x ^{5}})

Simplify

\frac{x ^{3}}{x ^{5}} : \frac{1}{x ^{2}}

= ln (\frac{1}{x ^{2}})

Apply log rule:

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

= - ln (x^{2})

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Frequently Asked Questions (FAQ)

What is ln(x^3)-5ln(x) ?
The solution to ln(x^3)-5ln(x) is -ln(x^2)