Hi,

I'm currently trying to solve for the following exponential equation: 3^(2x)-5(3^x)=-6

I'm hoping that someone can explain why the steps I took to solve this equation are incorrect:

line 1 -3^(2x)-5(3^x)=-6

line 2 -3^(2x)-15^x=-6

line 3 -3^x(1^x-5) = -6

line 4 -3^x(-4)=-6

line 5 -3^x=3/2

line 6 -xlog3=log(3/2)

line 7 -x=(log(3/2)/(log3)

line 8 -x=0.37...

The reason why I thought it was okay to remove the variable exponent from 1 after line 3 is because any exponent to 1 is just one. Which lead me to just subtract 5 from 1.

I am also familiar with another method of solving this, which is by letting 3^x equal a variable (e.g. let 3^x = u) and then solve the problem as if it is a quadratic equation. This method lead me to the correct answer. However, I still don't understand why the previous method does not work.