Question

7 ln x=21... solve?

Answer 1

7lnx=21

lnx=3
x=e^3
=20.0855369

Answer 2

so... did we just decide the 7 isn't in the equation anymore?

Answer 3

you divide both sides by 7

Answer 4

\[\mathrm{Divide\:both\:sides\:by\:}7\]
\[\frac{7\ln \left(x\right)}{7}=\frac{21}{7}\]
\[\ln \left(x\right)=3\]
\[\mathrm{Use\:the\:logarithmic\:definition:\quad }a=\ln \left(e^a\right)\]

\[3=\ln \left(e^3\right)\]
\[\ln \left(x\right)=\ln \left(e^3\right)\]

Answer 5

oooh right! Thank you so much!

Answer 6

\[\mathrm{When\:the\:logs\:have\:the\:same\:base:\:\:}\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\quad \Rightarrow \quad f\left(x\right)=g\left(x\right)\]
\[\mathrm{For\:}\ln \left(x\right)=\ln \left(e^3\right)\mathrm{,\:\quad solve\:}x=e^3\]
\[x=e^3\]
\[x=e^3\quad \left(\mathrm{Decimal:\quad }x=20.08554\right)\]

Answer 7

@study_buddy99 are you gotit