Question

What is the solution for this equation?

In(x+6)-in(2x-1)=0

answers in the image!

Answer 1

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`\sf ln(x+6)-ln(2x-1)=0\\\\\tt ln(x+6)=ln(2x-1)\\\\ \sf e^(ln(x+6))=e^(ln(2x-1))\\\\ \tt x+6=2x-1\\\\\sf 2x-1=6+1\\\\\bold x=7`

Answer 2

x=7

Explanation:

ln(x+6)-ln(2x-1)=0

add ln(2x-1) to each side

ln(x+6) = ln(2x-1)

Raise each side to the base e

e^ln(x+6) = e^ln(2x-1)

x+6 = 2x-1

Subtract x from each side

x+6-x = 2x-1-x

6 = x-1

Add 1 to each side

6+1 = x-1+1

7=x