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

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

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

Goten77Best ResponseYou've already chosen the best response.0
think bout it..... not that hard to read..... but it wont ever end....
 one year ago

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

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

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

Goten77Best ResponseYou've already chosen the best response.0
strange its basically a property..... memorable
 one year ago
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