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

1 Answer
Nov 4, 2016

Answer:

#x = ln18/ln9#

Explanation:

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!