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Popular >

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

Solution

simplify

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

Solution

ln (\frac{25 x ^{2}}{2})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{( 5 x ^{2} ) ^{2}}{2 x ^{2}} : \frac{25 x ^{2}}{2}

= ln (\frac{25 x ^{2}}{2})

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Frequently Asked Questions (FAQ)

What is 2ln(5x^2)-ln(2x^2) ?
The solution to 2ln(5x^2)-ln(2x^2) is ln((25x^2)/2)