SOLUTION: log[4](3x+1)=2

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Question 334146: log[4](3x+1)=2
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
log%284%2C+%283x%2B1%29%29+=+2
When the equation is logarithmic and the variable you are solving for is in the argument of the logarithm, the key is to rewrite the logarithmic equation in exponential form:
4%5E2+=+3x%2B1
which simplifies to:
16+=+3x+%2B+1
This is now a very simple equation to solve:
15+=+3x
5+=+x
With any logarithmic equation you should check your answers. You must ensure that no arguments of any logarithms become zero or negative!

Checking x = 5 in the original equation:
log%284%2C+%283x%2B1%29%29+=+2
log%284%2C+%283%285%29%2B1%29%29+=+2
log%284%2C+%2815%2B1%29%29+=+2
log%284%2C+%2816%29%29+=+2
The argument is positive to the solution checks!