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solve: 2^(x+1) = 3… - QuestionCove
OpenStudy (anonymous):

solve: 2^(x+1) = 3^(1-2x)

6 years ago
OpenStudy (anonymous):

\[log_e both sides \] \[xlog_e2 + log_e2 =log_e3 -2xlog_e3\] Solve this

6 years ago
myininaya (myininaya):

\[\ln(2^{x+1})=\ln(3^{1-2x})\] \[(x+1)\ln2=(1-2x)\ln3\] \[xln2+\ln2=\ln3-2xln3\] \[x(\ln2+2\ln3)=\ln3-\ln2\] \[x=\frac{\ln3-\ln2}{\ln2+2\ln3}\]

6 years ago
OpenStudy (anonymous):

\[(x+1)\ln(2)=(1-2x)\ln(3)\] and now a bunch of algebra

6 years ago
OpenStudy (anonymous):

\[x\ln(2)+\ln(2)=\ln(3)-2x\ln(3)\]

6 years ago
OpenStudy (anonymous):

and now look above!

6 years ago
myininaya (myininaya):

\[x=\frac{\ln(\frac{3}{2})}{\ln2+\ln9}=\frac{\ln(\frac{3}{2})}{\ln(2 \cdot 9)}=\frac{\ln(\frac{3}{2})}{\ln18}\]

6 years ago
OpenStudy (anonymous):

myininaya, are you the type that writes \[\ln3\] and \[\sin x\]?

6 years ago
myininaya (myininaya):

?

6 years ago
OpenStudy (anonymous):

i will report you to the math police

6 years ago
OpenStudy (anonymous):

\[\sin(x),\ln(x)\]

6 years ago
myininaya (myininaya):

i do it both ways

6 years ago
OpenStudy (anonymous):

\[\frac{\ln6}{\ln3}=2\]

6 years ago
OpenStudy (anonymous):

yes?

6 years ago
myininaya (myininaya):

no

6 years ago
OpenStudy (anonymous):

why not? cancel the 3, cancel the ln

6 years ago
myininaya (myininaya):

\[\frac{\ln9}{\ln3}=2\]

6 years ago
OpenStudy (anonymous):

no \[\frac{\ln 9}{\ln3}=3\]

6 years ago
myininaya (myininaya):

satellite why you always hating on me

6 years ago
myininaya (myininaya):

lol

6 years ago
OpenStudy (anonymous):

maybe, but if i have \[\frac{\ln(9)}{\ln(3)}\] then i know it is 2. otherwise i just cancel the ln and the 3 to get 3

6 years ago
OpenStudy (anonymous):

i like to give you a hard time, i will stop. ok i won't

6 years ago
OpenStudy (anonymous):

"why you be hatin'?"

6 years ago
myininaya (myininaya):

ln by itself makes no sense clearly when i say ln3 it also means ln(3)

6 years ago
OpenStudy (anonymous):

and when i say eggs i mean bacon

6 years ago
myininaya (myininaya):

no!

6 years ago
OpenStudy (anonymous):

LOL

6 years ago
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