What is ln((5e^{4x+3})/(3x+2)) ?

The solution to ln((5e^{4x+3})/(3x+2)) is ln(5)+4x+3-ln(3x+2)

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simplify ln((5e^{4x+3})/(3x+2))

simplify

ln (\frac{5 e ^{4 x + 3}}{3 x + 2})

ln (5) + 4 x + 3 - ln (3 x + 2)

Solution steps

ln (\frac{5 e ^{4 x + 3}}{3 x + 2})

Apply log rule:

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

ln (\frac{5 e ^{4 x + 3}}{3 x + 2}) = ln (5 e^{4 x + 3}) - ln (3 x + 2)

= ln (5 e^{4 x + 3}) - ln (3 x + 2)

Apply log rule:

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

ln (5 e^{4 x + 3}) = ln (5) + ln (e^{4 x + 3})

= ln (5) + ln (e^{4 x + 3}) - ln (3 x + 2)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{4 x + 3}) = (4 x + 3) ln (e)

= ln (5) + (4 x + 3) ln (e) - ln (3 x + 2)

(4 x + 3) ln (e) = 4 x + 3

= ln (5) + 4 x + 3 - ln (3 x + 2)

- lo g_{10} (3.6 \cdot 1 0^{- 11})

ln (\frac{a}{b ^{- 3}})

lo g_{4} (\frac{2}{100})

ln (3 e) + ln (e^{5}) + ln (e)

ln (2 e^{θ})

What is ln((5e^{4x+3})/(3x+2)) ?
The solution to ln((5e^{4x+3})/(3x+2)) is ln(5)+4x+3-ln(3x+2)