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Popular >

simplify ln((6x^2)/(y^4))

Solution

simplify

ln (\frac{6 x ^{2}}{y ^{4}})

Solution

ln (6) + 2 ln (x) - 4 ln (y)

Solution steps

ln (\frac{6 x ^{2}}{y ^{4}})

Apply log rule:

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

ln (\frac{6 x ^{2}}{y ^{4}}) = ln (6 x^{2}) - ln (y^{4})

= ln (6 x^{2}) - ln (y^{4})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (y^{4}) = 4 ln (y)

= ln (6 x^{2}) - 4 ln (y)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (6 x^{2}) = ln (6) + ln (x^{2})

= ln (6) + ln (x^{2}) - 4 ln (y)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= ln (6) + 2 ln (x) - 4 ln (y)

Popular Examples

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Frequently Asked Questions (FAQ)

What is ln((6x^2)/(y^4)) ?
The solution to ln((6x^2)/(y^4)) is ln(6)+2ln(x)-4ln(y)