Question

Can someone walk me through this question

solve 3^4x-5=(1/27)^2x+10 for x

Answer 1

https://prnt.sc/po5r4l

Answer 2

It's been awhile but I think you could ln both sides?

\(\Large ln( 3^{4x+5} ) = ln(\frac{1}{27} ^{2x+10} ) \)

\(\Large (4x+5) ln(3) = (2x+10) ln (\frac{1}{27} ) \)

Answer 3

Do you think you could continue from here? Or do you need more assistance?

Answer 4

Well, if you ever come back lol
I'll give ya the steps and what I did:

1) Bring down the exponents
2) distribute the ln
3) Get like terms on individual sides
4) Factor out an "x" from the one side
5) Divide to get the "x" by itself

It looked messy but actually came out nicely.

Answer 5

Although you could use natural log like any other, there's no need to here.


\( \frac {1}{27}\) can be written as \( 3^{-3} \). Substitute that in and you will get


\(3^{4x-5} = 3^{-3(2x+10)}\)

\(4x-5 = -3(2x+10)\)

Now simple algebra. You can find x.

Answer 6

so in exact form -2/5? I could do that as my answer?

Answer 7

oh nvm