Solve the following exponential equation.?

3x+10 = (4x+6) ln 39

= 4x ln 39 + 6 ln 39

x(4 ln 39 -3)=10-6 ln 39

x= (10 - 6 ln 39)/(4 ln 39 - 3)

= -1.03

e^(3x+10) = 39^(4x+6)

take the natural log of both sides

ln(e^(3x+10)) = ln(39^(4x+6))

(3x+10) = ln(39^(4x+6))

by the exponent/factor property of logarithms

(3x+10) = (4x+6)ln(39)

3x+10 = 4xln(39)+6ln(39)

3x - 4xln(39) = 6ln(39) - 10

x(3 - 4ln(39)) = 6ln(39) - 10

the exact answer is

x = (6ln(39) - 10) / (3 - 4ln(39))

the approximate answer is

-1.028069021

this can be verified using an MS Excel worksheet formula

=(6*LOG(39,EXP(1))-10)/(3-4*LOG(39,EXP(1)))

3x+10 = ln [ 39^(4x+6)] = (4x+6)ln39

x(3-4ln39) = [6ln39-10]

x = [6ln39-10]/(3-4ln39)

x = -1.02807

Rounds to

x = -1.03