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Solve for x: (2x)^(log(b) 2) = (3x)^(lo...

Solve for ` x: (2x)^(log_(b) 2) = (3x)^(log_(b)3)`.

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` (2x)^(log_(b) 2) = (3x)^(log_(b)3)`
` rArr log_(b) 2 [ log 2 + log x ]= log_(b) 3 [log3 + log x]`
` or (log_(b)2)(log 2) - log_(b)3*log 3 = (log_(b)3-log_(b) 2) log x`
` or (log 2)/(log b) * log 2 - (log 3)/(log b) * log 3 = ((log 3)/(logb)-(log 2)/(logb)) log x`
` or ((log 2)^(2) - (log 3)^(2))/(log b) = ((log 3 - log 2)/(log b)) log x `
` or log x =- (log 3 + log 2) = log (6)^(-1)`
` or x = 1//6`
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