How do you solve #3^(0.1x)-4=5#?

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Answer 1 · 2016-10-30T03:14:54

#x=20#

#3^(0.1x) -4=5#

Add #4# to both sides.

#3^(0.1x)=9#

Take the log of both sides.

#log 3^(0.1x)= log9#

Use the log rule #logx^a=alogx#

#0.1x log3=log9#

Divide both sides by #0.1 log3#

#x=log9/(0.1 log3)=(10log9)/log3#

Use the change of base formula #log_ba=loga/logb#

#x=10 * log_3 9#

#log_3 9 = color(red)2# because #3^color(red)2=9#

#x=10*color(red)2= 20#