solve the following exponential equation 62x6x1160Solution62

solve the following exponential equation 6^2x+6^x+1-16=0

6^2x + 6^(x+1) - 16 =0

Re write it as : (6^x)^2 + 6.6^(x) - 16 =0

Let 6^x =y

So, y^2 +6y -16 =0

y^2 +8y -2y -16 =0

y(y +8) -2 ( y +8 =0

(y -2)( y +8) =0

y = 2 and y = 8

6^x =2 ---> taking natural log of both sides:

xln6= ln2----> x =ln2/ln6 = 0.386

x = 0.386

y =8 ----> 6^x = 8

x*ln6 = ln8 ----> x = ln8/ln6 = 1.16

Solution : x = 0.386 , 1.16