Question

5^2x+1=3^4x-1
Find x.

Answer 1

\[5^{2x+1}=3^{4x-1}\]

Answer 2

Is x-1 included as a square root? I don't think so but just asking

Answer 3

It is, sadly - or else it would be much easier. I wasn't sure how to take logs of each side.

Answer 4

It's part of the power.

Answer 5

Let me try

Answer 6

I think its 2.3

Answer 7

Take log of each side is good start.

HINT: \(\log(a^n) = n\log(a)\)

So you should end up with \((2x+1)\ln(5) = (4x+1)\ln(3)\)

Answer 8

ln(5) and ln(3) are just constants, so now it's simple algebra.

make sense so far?

Answer 9

oops 4x-1*

but idea is same

Answer 10

final answer is going to be ugly lol...

Answer 11

@Vaudriel i have the steps if you want

Answer 12

I can show you steps so you will get it

Answer 13

Would you please? Thanks

Answer 14

What would you do after moving the exponents to the front of the terms?

Answer 15

Would you take ln of 5 and multiply it with (2x+1)?

Answer 16

yes take ln of 5

Answer 17

and then distribute parentheses

Answer 18

Okay, thanks!

Answer 19

got it ?? :O

Answer 20

Yeah, so I combine like terms and divide?