SOLUTION: Solve 4^2t = 5^4t+4] I get -2.5803 but i think I did something wrong.

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Question 615879: Solve 4^2t = 5^4t+4]
I get -2.5803 but i think I did something wrong.
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(57203) (Show Source):
You can put this solution on YOUR website!
Solve 4^2t = 5^4t+4]
---------
16^t = (5^4]^(t+1)
----
t*log(16) = (t+1)log(625)
----
t(log(16)) = t*log(625) + log(625)
---
t[log(16)-log(625)] = log(625)
---
t = -1.7565
====================
Cheers,
Stan H.
====================

Answer by solver91311(16868) (Show Source):
You can put this solution on YOUR website!

I have to presume you mean

Because the only way I know to solve

Is to find an approximate root by numerical methods.

Be that as it may, your intuition is spot on.

(order of magnitude difference)

Take the log of both sides (any base, doesn't matter)

Use

to write:

Multiply both sides by

Just for neatness sake, let

Then

The rest is just calculator (or better, spreadsheet) work.

John

My calculator said it, I believe it, that settles it