How do you solve #3^(x+4)=7^(2x-1)#?

1 Answer
MoominDave
Jun 28, 2018

Take logarithms

Explanation:

#3^(x+4)=7^(2x-1)#

Take logs:

#(x+4)log3=(2x-1)log7#
#x(log3-2log7)=-log7-4log3#

#x=(-log7-4log3)/(log3-2log7)=(log7+4log3)/(2log7-log3)#
#=(log7+log81)/(log49-log3)=log567/log(49/3)=log_(49/3)567#

To three significant figures, #x=2.27#.

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