Question

solve the equation \[2^{4x}=9^{x-1}\] and check

Answer 1

start with
\[4x\ln(2)=(x-1)\ln(9)\] and then do some algebra to solve for \(x\)

Answer 2

Thanks

Answer 3

@satellite73 uhh... i feel really stupid asking this but i bring the 4x and x-1 to one side right? and also the ln9 and ln2 to one side?
@Green52017 hm? lol you're welcome... ? :S

Answer 4

don't forget that \(\ln(9)\) and \(\ln(2)\) are constants, treat them like \(a\) and \(b\)

Answer 5

Why would you feel stupid but btw im not solving it its asking for a multiple choice im just stuff a lil bit i need a little bit of guidance lol

Answer 6

A)
Switch the x and y in the equation
B)
Change the slope of 2 to a slope of 3.
C)
Change the y-intercept of 2 to a y-intercept of 3.
D)
Change the y-intercept of 200 to a y-intercept of 3.

Answer 7

so first step is to multiply out on the right, get
\[4\ln(2)x=\ln(9)x-\ln(9)\] then maybe
\[4\ln(2)x-\ln(9)x=-\ln(9)\]
\[(4\ln(2)-\ln(9))x=-\ln(9)\] and finally
\[x=\frac{-\ln(9)}{4\ln(2)-\ln(9)}\]
there are other way you can write it

Answer 8

how did you get 4ln(2)x ... ? ._.

Answer 9

and ln(9)x

Answer 10

dont forget they are constants
suppose you wanted to solve
\[4\times x\times A=(x-1)\times B\] for \(x\) what would you do?

Answer 11

first multiply out on the right, and rewrite the left as
\[4Ax=Bx-B\] then all terms with \(x\) on the left get \(4Ax-Bx=-B\)
then factor out the \(x\) get \((4A-B)x=-B\) and finally divide get
\[x=\frac{-B}{4A-B}\]

Answer 12

replace \(A\) by \(\ln(2)\) and \(B\) by \(\ln(9)\) and you get the same thing

Answer 13

okay. uhm just one last question, the sheet tells me that the asnwer is x= - log 9/log(16/9)
would it be th same as ssaying x=−ln(9)/4ln(2)−ln(9)

Answer 14

yes because
\[4\ln(2)=\ln(2^4)=\ln(16)\]

Answer 15

and
\[\ln(16)-\ln(9)=\ln(\frac{16}{9})\] as i said there are other ways to write it

Answer 16

YAY! okay thank you :)

Answer 17

yw