What is 2ln(2)+2β+2ln(x)+3e^βx ?

The solution to 2ln(2)+2β+2ln(x)+3e^βx is ln(4x^2)+2β+3e^βx

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simplify 2ln(2)+2β+2ln(x)+3e^βx

simplify

2 ln (2) + 2 β + 2 ln (x) + 3 e^{β} x

ln (4 x^{2}) + 2 β + 3 e^{β} x

Solution steps

2 ln (2) + 2 β + 2 ln (x) + 3 e^{β} x

Apply log rule:

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

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

= ln (2^{2}) + 2 β + 2 ln (x) + 3 e^{β} x

Apply log rule:

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

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

= ln (2^{2}) + 2 β + ln (x^{2}) + 3 e^{β} x

Apply log rule:

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

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

= ln (2^{2} x^{2}) + 2 β + 3 e^{β} x

2^{2} = 4

= ln (4 x^{2}) + 2 β + 3 e^{β} x

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What is 2ln(2)+2β+2ln(x)+3e^βx ?
The solution to 2ln(2)+2β+2ln(x)+3e^βx is ln(4x^2)+2β+3e^βx