What is ln(3(x+2))-(ln(x+2))/2 ?

The solution to ln(3(x+2))-(ln(x+2))/2 is ln(3)+(ln(x+2))/2

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simplify ln(3(x+2))-(ln(x+2))/2

simplify

ln (3 (x + 2)) - \frac{ln ( x + 2 )}{2}

ln (3) + \frac{ln ( x + 2 )}{2}

Solution steps

ln (3 (x + 2)) - \frac{ln ( x + 2 )}{2}

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (3 (x + 2)) = ln (3) + ln (x + 2)

= ln (3) + ln (x + 2) - \frac{ln ( x + 2 )}{2}

Convert element to fraction:

ln (x + 2) = \frac{ln ( x + 2 ) 2}{2}

= - \frac{ln ( x + 2 )}{2} + \frac{ln ( x + 2 ) \cdot 2}{2}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- ln ( x + 2 ) + ln ( x + 2 ) \cdot 2}{2}

Add similar elements:

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

= ln (3) + \frac{ln ( x + 2 )}{2}

ln (x - 3) - 2 ln (x + 12) - ln (x)

3 ln (x^{2}) - ln (x)

ln (- e^{- y} (y + 1))

- ln (\frac{80}{81})

ln (\frac{52}{7})

What is ln(3(x+2))-(ln(x+2))/2 ?
The solution to ln(3(x+2))-(ln(x+2))/2 is ln(3)+(ln(x+2))/2