2023 UPDATED!!! Solve 3 log6 2 + 2 log6 3 − log6 x = 2.

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Solve 3 log6 2 + 2 log6 3 − log6 x = 2.

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$D: x textgreater 0 \\ 3 log_62 + 2 log_63- log_6x = 2 \ ----------------------- Usage: \ log_ab = c iff a ^ c = b \ log_ab + log_ac = log_a (bc) \ log_ab- log_ac = log_a ( frac {b} {c}) log_ab ^ c = c log_ab \ ----------------------- \ log_62 ^ 3 + log_63 ^ 2- log_6x = 2 \\ log_68 + log_69- log_6x = log_66 ^ 2 \\ log_6 (8 cdot9) - log_6x = log_636 \\ log_672- log_6x = log_636 \\ log_6 frac {72} {x} = log_636 iff dfrac {72} {x} = 36 \\ dfrac {x} {72} = dfrac {1} {36} | multiply both sides by 72 \\ x = dfrac {72} {36} \\ boxed {x = 2} in D$