Question

Question #db07d

Answer 1

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...)