I am going to use another way to solve this equation.
aftenn provided a good start, Substitute x = ln a.......
ex+34e−x+5=2ex+3=8ex+10elna+3=8elna+10a+3=8a+10a=8a+7a2−7a−8=0(a+1)(a−8)=0(ex+1)(ex−8)=0Set each factor to 0ex=−1 have no real solutionsPS: x=πi is a solution but it's not realex=8x=ln8
If you want imaginary solutions too x = pi(i) or x = ln 8
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