(I am missing out base 1/2 and making a correction to your question)

log x² - 3 log x + 5 = 3² ( log (base 3) 9 =2 )

log x² - 3 log x = 9 -5 =4

2 log x - 3 log x = 4

- log x = 4

log x = -4

x = (1/2)^-4

X = 16

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