SOLUTION: Log7(3x)+log7(2x-1)=log7(16x-10)

Question 1202488: Log7(3x)+log7(2x-1)=log7(16x-10)
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answers: and

Work Shown:

All logs for this problem are base 7
log(3x) + log(2x-1) = log(16x-10)
log(3x*(2x-1)) = log(16x-10) ..... log rule log(A)+log(B) = log(A*B)
3x*(2x-1) = 16x-10
6x^2-3x = 16x-10
6x^2-3x-16x+10 = 0
6x^2-19x+10 = 0

Now use the quadratic formula
a = 6
b = -19
c = 10

or

or

or

From here we need to check each possible solution.
I'll let the student do this part. Plug each x value one at a time into the original equation. Simplify both sides.
You should find that both x values work.

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