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Popular >

simplify ln(x^5)-2ln(sqrt(x^3))

Solution

simplify

ln (x^{5}) - 2 ln (x^{3})

Solution

ln (x^{2})

Solution steps

ln (x^{5}) - 2 ln (x^{3})

Apply log rule:

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

2 ln (x^{3}) = ln ((x^{3})^{2})

= ln (x^{5}) - ln ((x^{3})^{2})

Apply log rule:

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

ln (x^{5}) - ln ((x^{3})^{2}) = ln \frac{x ^{5}}{( x ^{3} ) ^{2}}

= ln \frac{x ^{5}}{( x ^{3} ) ^{2}}

Simplify

\frac{x ^{5}}{( x ^{3} ) ^{2}} : x^{2}

= ln (x^{2})

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Frequently Asked Questions (FAQ)

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