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...)