Exponential equation

[winkylocc]

I have a problem I'm posting here. I already have the answer that Im posting as well along with the steps that the instructor wrote next to my incorrect answer. I need help with one of the steps that completely lost me.
Here is the problem:

5 ^2x+1 = 7 ^3-x

The steps follow:

2x+1 = (3-x) log ₅ 7
What he does next with the (3-x) is what really throws me:
2x+1 = 3 log₅ 7 - x log ₅ 7

2x + x log ₅ 7 = 3 log ₅ 7 - 1

x(2 + log ₅ 7) = 3 log ₅ 7 - 1

The answer is:

x = 3 log ₅ 7 -1

2 + log ₅ 7

Again, I was with him until the right side of the second step where things started happening that I cant figure out. Thanks for the help.

[stapel_eliz]

5 ^2x+1 = 7 ^3-x

2x+1 = (3-x) log ₅ 7

What he does next with the (3-x) is what really throws me:

2x+1 = 3 log₅ 7 - x log ₅ 7

He just distributed, like this:

. . . . .(3 - x)y = 3(y) - x(y) = 3y - xy

[winkylocc]

How will I know to distribute in a problem like that.

[stapel_eliz]

How will I know to distribute in a problem like that.

Sometimes distributing is helpful; sometimes factoring is helpful. In general, use the step(s) you need for isolating the variable.