How do you solve $e^{3 x} = 20$ $e^(3x)=20$ ?

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Answer 1 · 2016-05-14T16:58:30

$\approx 1$ $~~1$

$e^{3 x} = 20$ $e^(3x)=20$

Taking ${log}_{e}$ $log_e$ on both sides we have
$e^{3 x} = 20$ $e^(3x)=20$

$\Rightarrow {log}_{e} e^{3 x} = {log}_{e} 20$ $=>log_ee^(3x)=log_e20$

$\Rightarrow (3 x) {log}_{e} e = {log}_{e} 20$ $=>(3x)log_ee=log_e20 " "$ using formula ${log}_{e} m^{n} = n {log}_{e} m$ $log_em^n=nlog_em$

$\Rightarrow (3 x) = {log}_{e} 20$ $=>(3x)=log_e20 " "$ since ${log}_{e} e = 1$ $log_ee=1$

$\Rightarrow x = \frac{{log}_{e} 20}{3} \approx \frac{3}{3} = 1$ $=>x=log_e20/3 ~~3/3=1$

How do you solve e3x=20e^(3x)=20?