Solve for x: Ln(3x+2) - lnx = 2

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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Given the logarithmic equation:

`ln(3x+2) - lnx = 2`

First we will use the logarithm properties to write as a single log.

==> We know that:

`lna - lnb = ln (a/b) `

`==gt ln(3x+2) - lnx = ln((3x+2)/x) = 2`

Now we will rewrite in exponent form.

`==gt (3x+2)/x = e^2 `

`==gt 3x + 2 = e^2*x `

`==gt 3x -e^2*x = -2 `

`==gt (3-e^2) x = -2 `

`==gt x = -2/(3-e^2) ~~ 0.4557`

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