What is ln| 7/5+(3x)/5 |-ln|-3/5+3/5 x| ?

The solution to ln| 7/5+(3x)/5 |-ln|-3/5+3/5 x| is ln((|7+3x|)/(|-3+3x|))

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simplify ln| 7/5+(3x)/5 |-ln|-3/5+3/5 x|

simplify

ln \frac{7}{5} + \frac{3 x}{5} - ln - \frac{3}{5} + \frac{3}{5} x

ln (\frac{∣ 7 + 3 x ∣}{∣ - 3 + 3 x ∣})

Solution steps

ln \frac{7}{5} + \frac{3 x}{5} - ln - \frac{3}{5} + \frac{3}{5} x

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln \frac{7}{5} + \frac{3 x}{5} - ln - \frac{3}{5} + \frac{3}{5} x = ln (\frac{\frac{3 x}{5} + \frac{7}{5}}{\frac{3}{5} x - \frac{3}{5}})

= ln (\frac{\frac{7}{5} + \frac{3 x}{5}}{- \frac{3}{5} + \frac{3}{5} x})

Simplify

\frac{\frac{7}{5} + \frac{3 x}{5}}{- \frac{3}{5} + \frac{3}{5} x} : \frac{∣ 7 + 3 x ∣}{∣ - 3 + 3 x ∣}

= ln (\frac{∣ 7 + 3 x ∣}{∣ - 3 + 3 x ∣})

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ln (\frac{12}{12 + d})

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What is ln| 7/5+(3x)/5 |-ln|-3/5+3/5 x| ?
The solution to ln| 7/5+(3x)/5 |-ln|-3/5+3/5 x| is ln((|7+3x|)/(|-3+3x|))