SOLUTION: Can you help me solve this problem Solve. Log5 (3x+1)- Log5 4=2

Question 816636: Can you help me solve this problem
Solve. Log5 (3x+1)- Log5 4=2
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

First, use the property to combine the logs:

Then rewrite the equation in exponential form. In general is equivalent to . Using this pattern on our equation we get:

which simplifies to:

Now we solve this. Multiplying each side by 4 (to eliminate the fraction):
3x + 1 = 100
Subtracting 1:
3x = 99
Dividing by 3:
x = 33

Last, we check. This is not optional! A check must be made to ensure that the "solution(s)" make all bases and arguments of all logs valid. (Valid bases are any positive number except 1 and valid arguments are positive.) Any "solution" that makes any base or any argument invalid must be rejected.

Use the original equation to check:

Checking x = 33:

We can already see that the bases are 5's and the arguments are (or will end up) positive -- both valid. So this solution checks!
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