Solve the following exponential equation Express your answer

Solve the following exponential equation. Express your answer as both an exact expression and a decimal approximation rounded to two decimal places. Use e = 2.71828182845905. e^3x - 8 = 91^2x + 7 If you wish to enter log () or ln(), you must use the keypad. X = almostequalto

Solution

by properties of logaritham e^a=b^m <=> a=ln(b^m) ,ln(b^m)=m*ln(b)

given e^3x-8=91^2x+7

=>3x-8=ln91^2x+7

=>3x-8=(2x+7)ln91

=>3x-8=(x2ln91)+(7ln91)

=>3x-(x2ln91)=8+(7ln91)

=>x(3-2ln91)=(8+ 7ln91)

=>x=(8+ 7ln91)_/(3-2ln91)

=>x=-6.57