What is 2ln(y)+3ln(5y) ?

The solution to 2ln(y)+3ln(5y) is ln(125y^5)

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simplify 2ln(y)+3ln(5y)

simplify

2 ln (y) + 3 ln (5 y)

ln (125 y^{5})

Solution steps

2 ln (y) + 3 ln (5 y)

Apply log rule:

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

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

= ln (y^{2}) + 3 ln (5 y)

Apply log rule:

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

3 ln (5 y) = ln ((5 y)^{3})

= ln (y^{2}) + ln ((5 y)^{3})

Apply log rule:

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

ln (y^{2}) + ln ((5 y)^{3}) = ln (y^{2} (5 y)^{3})

= ln (y^{2} (5 y)^{3})

Simplify

y^{2} (5 y)^{3} : 125 y^{5}

= ln (125 y^{5})

ln (x + h) - ln (x)

ln (\frac{3 x}{7})

lo g_{5} (\frac{3 x ^{3} ( 1 - 2 x ) ^{6}}{2 x ^{y} ( x ^{2} - y ^{2} )})

5 ln (2) + 7 ln (x) + 4 ln (y)

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