Find the exact solutions, in their simplest form, to the equations : a) 2ln(2x + 1)-4=0 b)7^(x)e^(4x)=e^5

a) 2ln(2x + 1)-4=0

-> ln(2x + 1)-2=0

-> ln(2x + 1)=2

-> (2x + 1)=e2

-> 2x = e-1

-> x = (e-1)/2

b) 7xe4x=e5

-> 7x=e\ e4x

​​​​​​​-> 7x=e5-4x

​​​​​​​-> ln(7x)=5-4x

​​​​​​​-> xln(7)=5-4x

​​​​​​​-> x(ln(7)+4)=5

​​​​​​​-> x=5/(ln(7)+4)

Answered by Elizabeth L. Maths tutor

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