How Do You Isolate x in a Natural Logarithm Equation?

[buzzingbee]

Solve the following equation for x

16-12ln(7x)=47

I know I need to isolate x . however I am unsure how to get ln(7x) separated.

what i have so far

ln(7x)=-31/12

 

[SteamKing]

e^(ln(y)) = y

e = 2.71828...

 

[HallsofIvy]

You always solve an equation for a variable such as x by doing the reverse of what has been done to it (to both sides, of course).

If you were asked to evaluate 23- 9ln(4x) (I am using different numbers so you can apply the same idea to your problem) for a given value of x, you would:
1) multiply by 4: 4x.
2) take the natural logarithn: ln(4x)
3) multiply by -9: -9 ln(7x)
4) add 23: 23- 12 ln(7x)

To solve for x, do the opposite: do the opposite of each step, in the opposite order. The opposite of "add 23" is "subtract 23", the opposite of "multiply by -9" is "divide by -9", the opposite of "multiply by 4" is "divide by 4", and the opposite of "take the natural logarithm" is "take the exponential".

Starting from 23- 9 ln(4x)= 85:
1) subtract 23: 23- 9ln(4x)- 23= 84- 23, -9ln(4x)= 61
2) divide by -9: -9ln(4x)/(-9)= 61/(-9), ln(4x)= -61/9
3) take the exponential: e^ln(4x)= e^-61/9: 4x= e<sup>- 61/9[/tex]
4) divide by 4: 4x/4= e-61/9/4, x= e-61/9/4.

You will need to use a calculator to actually evaluate e-61/9.</sup>