SOLUTION: Good evening, I need your help to solve for the exponent t. 5^t = 7^(t+1). I started with t log 5 = (t+1) log 7. So, I tried deducting (t+1) from both sides and then divide lo

Question 21192: Good evening,
I need your help to solve for the exponent t. 5^t = 7^(t+1). I started with t log 5 = (t+1) log 7. So, I tried deducting (t+1) from both sides and then divide log 7 from both sides, but didn't really understand.
Please help.
Joanna
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
hello Joanne,

this is a fairly straight forward algebraic manipulation question. Nothing to be wary of, really. Just be careful what you do:

--> take logs (base10, whatever :-) )
tlog5 = (t+1)log7
tlog5 = tlog7 + log7
tlog5 - tlog7 = log7
t(log5 - log7) = log7
t = log7/(log5 - log7) is your answer
i would recommend that you ALWAYS work out the answer on your calculator (here it is, -5.78327) and then put that back into the question to check that the left and right hand sides do actually agree. Then you will know for certain, that the answer is correct.

PS, keep your answer to several decimal places to avoid horrendous rounding errors.

hope this helps

jon.

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