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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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