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 = e² -1

-> x = (e² -1)/2

b) 7^xe^4x=e⁵

-> 7^x=e⁵ \ e^4x

​​​​​​​-> 7^x=e^5-4x

​​​​​​​-> ln(7^x)=5-4x

​​​​​​​-> xln(7)=5-4x

​​​​​​​-> x(ln(7)+4)=5

​​​​​​​-> x=5/(ln(7)+4)