How do you solve #3^x=3sqrt2#?

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Answer 1 · 2016-11-04T01:05:19

#x = ln18/ln9#

Take the natural logarithm of both sides.

#ln(3^x) = ln(3sqrt(2))#

Use the logarithm rule #lna^n = nlna#.

#xln3 = ln(3sqrt(2))#

#xln3 = ln(sqrt(18))#

Use the same logarithm rule as above.

#x = ln(18)^(1/2)/ln3#

#x= (1/2ln18)/ln3#

#x = ln18/(2ln3)#

#x = ln18/ln9#

Hopefully this helps!