What is ln((210e^x)/(4.1+1.2e^x)) ?

The solution to ln((210e^x)/(4.1+1.2e^x)) is ln(210)+x-ln(4.1+1.2e^x)

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simplify ln((210e^x)/(4.1+1.2e^x))

simplify

ln (\frac{210 e ^{x}}{4.1 + 1.2 e ^{x}})

ln (210) + x - ln (4.1 + 1.2 e^{x})

Solution steps

ln (\frac{210 e ^{x}}{4.1 + 1.2 e ^{x}})

Apply log rule:

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

ln (\frac{210 e ^{x}}{4.1 + 1.2 e ^{x}}) = ln (210 e^{x}) - ln (4.1 + 1.2 e^{x})

= ln (210 e^{x}) - ln (1.2 e^{x} + 4.1)

Apply log rule:

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

ln (210 e^{x}) = ln (210) + ln (e^{x})

= ln (210) + ln (e^{x}) - ln (1.2 e^{x} + 4.1)

Apply log rule:

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

ln (e^{x}) = x ln (e)

= ln (210) + x ln (e) - ln (4.1 + 1.2 e^{x})

x ln (e) = x

= ln (210) + x - ln (1.2 e^{x} + 4.1)

ln (\frac{21}{2 x}) - ln_{4} (21)

\frac{1}{6} ln (\frac{x - 3}{x + 3})

ln (\frac{x}{5}) + \frac{x ^{2}}{25}

lo g_{3} (2 (ab)^{3} c)

- ln (x y) ln (x) + \frac{1}{2} ln^{2} (x) - 2 ln (x)

What is ln((210e^x)/(4.1+1.2e^x)) ?
The solution to ln((210e^x)/(4.1+1.2e^x)) is ln(210)+x-ln(4.1+1.2e^x)