Question #db07d

1 Answer
Feb 10, 2018

I got #log(21)/log(9/7)~~12.11439573#

Explanation:

Take the log of both sides

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

Use the exponent rule to bring down the exponents

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

Distribute

#2xlog3-log3=xlog7+log7#

Move the "x" terms to one side of the equation, constant terms to the other:

#2xlog3-xlog7=log7+log3#

Factor out the #x# on the left side

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

Isolate #x# by dividing

#x=(log7+log3)/(2log3-log7)#

If all you need is the decimal answer, put that into your calculator and you should get #x~~12.11439573#. If you need the exact answer, simplify the logs using laws of logarithims.

#x=log(7*3)/log(3^2/7)=log(21)/log(9/7)#

(I don't think that simplifies any more...)