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 one year ago
Find the value of x and y:\[ (2x)^{\ln 2} = (3y)^{\ln 3} \]\[ 3^{\ln x} = 2^{\ln y}\]
 one year ago
Find the value of x and y:\[ (2x)^{\ln 2} = (3y)^{\ln 3} \]\[ 3^{\ln x} = 2^{\ln y}\]

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wio
 one year ago
Best ResponseYou've already chosen the best response.2Is this a system of equations?

wio
 one year ago
Best ResponseYou've already chosen the best response.2.... @Goten77 hard to read it... what are you doing?

Goten77
 one year ago
Best ResponseYou've already chosen the best response.0think bout it..... not that hard to read..... but it wont ever end....

wio
 one year ago
Best ResponseYou've already chosen the best response.2\[ \large \begin{array}{rcl} (2x)^{\ln2}&=&(3y)^{\ln3} \\ \ln(2x)\ln(2)&=&\ln(3y)\ln(3) \\ \ln(2)\ln(2) +\ln(2) \ln(x) &=&\ln(3)\ln(y)+\ln(3)\ln(3) \\ \ln(2) \ln(x)  \ln(3)\ln(y) &=&\ln(3)\ln(3)\ln(2)\ln(2) \end{array} \] \[ \large \begin{array}{rcl} 3^{\ln x}&=&2^{\ln y} \\ \ln(3)\ln (x)&=&\ln(2)\ln (y) \\ \ln(3)\ln (x)  \ln(2)\ln (y) &=& 0 \end{array} \] \[ \begin{bmatrix} \ln(2)&\ln(3) \\ \ln(3)& \ln(2) \end{bmatrix} \begin{bmatrix} \ln(x) \\ \ln(y) \end{bmatrix} = \begin{bmatrix} \ln(3)\ln(3)\ln(2)\ln(2) \\ 0 \end{bmatrix} \]

wio
 one year ago
Best ResponseYou've already chosen the best response.2If you put it into a matrix, it's not as big a mess.

wio
 one year ago
Best ResponseYou've already chosen the best response.2then at the very end raise it to the power of \(e\). It could be a singular matrix though?

Goten77
 one year ago
Best ResponseYou've already chosen the best response.0strange its basically a property..... memorable
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