Question

log (x-6) + log (x-3) = 2log2
Find X
Answer is 2 or 7​

Answer 1

Answer:

$log(x - 6) + log(x - 3) = 2 log(2) \\ \\ log((x - 6)(x - 3)) = log( {2}^{2} ) \\ \\ log( {x}^{2} - 9x + 18) = log(4) \\ \\ {x}^{2} - 9x + 18 = 4 \\ \\ {x}^{2} - 9x + 14 = 0 \\ \\ {x}^{2} - 7x - 2x + 14 = 0 \\ \\ x(x - 7) - 2(x - 7) = 0 \\ \\ (x - 2)(x - 7) = 0 \\ \\ x = 2 \\ is \: not \: possible \: as \: negative \: logs \:are \: never \: found \\ \\ therefore \\ x = 7 \: is \: the \: required \: answer \\ \\ formulae \\ \\ log( \alpha ) + log( \beta ) = log( \alpha \beta ) \\ \\ \alpha log( \beta ) = log( { \beta }^{ \alpha } )$

Step-by-step explanation:

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