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We have to solve for x given that log(2) x + log(3) x = 1

log(2) x + log(3) x = 1

take the log to the base 10

log x/log 2 + log x /log 3 = 1

=> log 3 * log x + log 2 * log...

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We have to solve for x given that log(2) x + log(3) x = 1

log(2) x + log(3) x = 1

take the log to the base 10

log x/log 2 + log x /log 3 = 1

=> log 3 * log x + log 2 * log x = log 2* log 3

=> log x ( log 2 + log 3) = log 2* log 3

=> log x = (log 2* log 3)/( log 2 + log 3)

=> log x = (log 2 * log 3)/log 6

=> x = 10^[(log 2* log 3)/log 6]

The value of x = 10^[(log 2* log 3)/log 6]

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