What is ln((4t}{x^2}*e^{-\frac{2t)/x}) ?

The solution to ln((4t}{x^2}*e^{-\frac{2t)/x}) is 2ln(2)+ln(t)-2ln(x)-(2t)/x

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simplify ln((4t}{x^2}*e^{-\frac{2t)/x})

simplify

ln (\frac{4 t}{x ^{2}} \cdot e^{- \frac{2 t}{x}})

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

Solution steps

ln (\frac{4 t}{x ^{2}} e^{- \frac{2 t}{x}})

Apply log rule:

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

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

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

Apply log rule:

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

ln (e^{- \frac{2 t}{x}}) = - \frac{2 t}{x} ln (e)

= ln (\frac{4 t}{x ^{2}}) - \frac{2 t}{x} ln (e)

Apply log rule:

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

ln (\frac{4 t}{x ^{2}}) = ln (4 t) - ln (x^{2})

= ln (4 t) - ln (x^{2}) - ln (e) \frac{2 t}{x}

Apply log rule:

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

ln (x^{2}) = 2 ln (x)

= ln (4 t) - 2 ln (x) - \frac{2 t}{x} ln (e)

Apply log rule:

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

ln (4 t) = ln (4) + ln (t)

= ln (4) + ln (t) - 2 ln (x) - ln (e) \frac{2 t}{x}

\frac{2 t}{x} ln (e) = \frac{2 t}{x}

= ln (4) + ln (t) - 2 ln (x) - \frac{2 t}{x}

ln (4) = 2 ln (2)

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

ln (c e^{c})

- lo g_{10} (8.83 \cdot 1 0^{- 3})

ln ((2 e^{b d} cosh (b u h) + 1)^{N})

ln (\frac{1}{81})

0.5 ln (100) - 2 ln (x) + 8 ln (y)

What is ln((4t}{x^2}*e^{-\frac{2t)/x}) ?
The solution to ln((4t}{x^2}*e^{-\frac{2t)/x}) is 2ln(2)+ln(t)-2ln(x)-(2t)/x