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

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve 4^2t = 5^4t+4] I get -2.5803 but i think I did something wrong.       Log On

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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