What is e^{(3^2-1)}*3^3+ln(5*3^3)*3^2+15 ?

The solution to e^{(3^2-1)}*3^3+ln(5*3^3)*3^2+15 is 27e^8+9ln(5)+27ln(3)+15

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simplify e^{(3^2-1)}3^3+ln(53^3)*3^2+15

simplify

e^{(3^{2} - 1)} \cdot 3^{3} + ln (5 \cdot 3^{3}) \cdot 3^{2} + 15

27 e^{8} + 9 ln (5) + 27 ln (3) + 15

Decimal Notation

80545.01312 \dots

Solution steps

e^{(3^{2} - 1)} \cdot 3^{3} + ln (5 \cdot 3^{3}) \cdot 3^{2} + 15

Apply log rule:

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

ln (5 \cdot 3^{3}) \cdot 3^{2} = 3^{2} ln (5) + 3^{2} ln (3^{3})

= 3^{3} e^{(3^{2} - 1)} + 3^{2} ln (5) + 3^{2} ln (3^{3}) + 15

Apply log rule:

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

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

= e^{3^{2} - 1} \cdot 3^{3} + 3^{2} ln (5) + 3^{2} \cdot 3 ln (3) + 15

e^{3^{2} - 1} \cdot 3^{3} = 3^{3} e^{8}

3^{2} \cdot 3 ln (3) = 3^{3} ln (3)

= 3^{3} e^{8} + 3^{2} ln (5) + 3^{3} ln (3) + 15

3^{3} = 27

= 27 e^{8} + 3^{2} ln (5) + 3^{3} ln (3) + 15

3^{2} = 9

= 27 e^{8} + 9 ln (5) + 3^{3} ln (3) + 15

3^{3} = 27

= 27 e^{8} + 9 ln (5) + 27 ln (3) + 15

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What is e^{(3^2-1)}*3^3+ln(5*3^3)*3^2+15 ?
The solution to e^{(3^2-1)}*3^3+ln(5*3^3)*3^2+15 is 27e^8+9ln(5)+27ln(3)+15