How do you solve $5e ^ { 5x } = 1890$ ?

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Answer 1 · 2017-04-18T20:06:05

$x approx1.864$

The Equation is $5e^(5x)=1890$

Dividing by 5 on both sides we get :

$e^(5x)=378$

Take natural log on both sides:

$ln(e^(5x))=ln(378)$

( using property $ln(a^b)=bln(a)$ )

$5xln(e)=ln(378)$

As $ln(e)=1$

$5x=ln (378)$

$5x=ln(2*3*3*3*7)$ (factorized 378)

(using property $ln(a*b*c)=ln(a) + ln(b) + ln(c)$ )

$5x=ln(2) +3ln(3) + ln(7)$

$x=1/5 (ln(2) +3ln(3) + ln(7))$

$x= 1/5 (.693 + 3(1.098) + 1.945)$

$x approx1.864$

How do you solve 5e ^ { 5x } = 18905e ^ { 5x } = 1890?