Part 1:
Apply exponent logarithm property for the first element:
4Log(3)+Log(2)= Log(3^4)+Log(2)
Now, apply the logarithm propery for a sum or multiplication and then solve it:
Log(2*3^4)= Log(162) = 2.21
Part 2:
20^x=e^(x+3)
Apply Ln for both sides:
Ln(20^x)=Ln(e^(x+3))
Apply exponet logarithm property in both sides:
x*Ln(20)=(x+3)*Ln(e), we know Ln(e)=1, so replace that and solve for x:
x*Ln(20)=x+3
x*Ln(20)-x=3
x(Ln(20)-1)=3
x=3/(Ln(20)-1)
x=3/(2.9957-1) = 3/1.9957
x=1.5032
