(1)If $\displaystyle a^{2x-1}=b^{1-3y}$ and $\displaystyle a^{3x-1}=b^{2y-2}$, prove that $\displaystyle 13xy-7x-5y+3=0$ Thanks for any help .
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Dear mathaddict, If $\displaystyle a^{2x-1}=b^{1-3y}$ than $\displaystyle (2x-1)ln(a)=(1-3y)ln(b)$ so $\displaystyle ln(a)/ln(b) = (1-3y)/(2x-1)$ Express the ln(a)/ln(b) from the other equation also and compare the two expression.
Thanks Skalkaz , but is there any other way besides that .
Originally Posted by mathaddict (1)If $\displaystyle a^{2x-1}=b^{1-3y}$ and $\displaystyle a^{3x-1}=b^{2y-2}$, prove that $\displaystyle 13xy-7x-5y+3=0$ Can this question be solved by just using laws of exponents and logarithms ?
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