How do you solve $18 = e^{3 x}$ $18=e^(3x)$ ?

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Answer 1 · 2016-12-24T14:14:00

$x = 0.963 (3 s . f .)$ $x = 0.963 ( 3 s.f.)$

$18 = e^{3 x}$ $18 = e^(3x)$

convert into a logarithmic function:

e.g. ${log}_{10} (100) = 2$ $log_10(100)=2$
$\to 10^{2} = 100$ $-> 10^2 = 100$

$18 = e^{3 x}$ $18 = e^(3x)$
$\to {log}_{e} (18) = 3 x$ $-> log_e(18) = 3x$

${log}_{e} (n) = ln (n)$ $log_e(n) = ln(n)$

enter $\to ln (18)$ $-> ln(18)$ into a calculator:

$\to ln (18) = 2.89037 . .$ $-> ln(18) = 2.89037..$

$3 x = 2.8903717578961647$ $3x = 2.8903717578961647$

divide this answer by $3$ $3$ :

$x = 0.963 (3 s . f .)$ $x = 0.963 ( 3 s.f.)$

How do you solve 18=e3x18=e^(3x)?