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QUESTION

# How do you express in terms of ln2 and ln3 given ln 3 sqrt 2?

ln(3sqrt(2)) = ln(3) + 1/2ln(2)

Using the properties that ln(ab) = ln(a) + ln(b) and ln(a^x) = xln(a), we have:

ln(3sqrt(2)) = ln(3)+ln(sqrt(2))

=ln(3) + ln(2^(1/2))

=ln(3) + 1/2ln(2)