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Popular >

simplify 4ln(2y)+2ln(y)

Solution

simplify

4 ln (2 y) + 2 ln (y)

Solution

ln (16 y^{6})

Solution steps

4 ln (2 y) + 2 ln (y)

Apply log rule:

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

4 ln (2 y) = ln ((2 y)^{4})

= ln ((2 y)^{4}) + 2 ln (y)

Apply log rule:

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

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

= ln ((2 y)^{4}) + ln (y^{2})

Apply log rule:

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

ln ((2 y)^{4}) + ln (y^{2}) = ln (y^{2} (2 y)^{4})

= ln (y^{2} (2 y)^{4})

Simplify

(2 y)^{4} y^{2} : 16 y^{6}

= ln (16 y^{6})

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Frequently Asked Questions (FAQ)

What is 4ln(2y)+2ln(y) ?
The solution to 4ln(2y)+2ln(y) is ln(16y^6)