Need , 1. write as a single logarithm. 4 ∙ log3 + log2 2. solve. give both the exact answer and approximate answer for x. the equation is in the attachment below.

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

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