Would I multiply the entire problem by 2?
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No, I don't think so. I would focus on the logarithm on the RHS. You can break that up according to the rules of logarithms.
t/2 = log(base2)3 + log(base2)2^t/3
Simplify using more logarithm rules. What do you get?
t/2 = log(base2)3 + t/3 log(base2)2
Keep going! You're 99.99% done.
t/2 = log(base2)3 + t/3
So, t = ...
For some reason I'm lost all of a sudden.
Bring the t/3 over to the LHS (to get all the t's on one side.)
t/2 - t/3 = log(base2)3
Yep. Keep going!
t/6 = log(base2)3 t =6 log(base2)3
Yeah, finally it's solved. I concluded that the answer is approximately 9.51 hours. I can't thank you enough for bearing with me and guiding me step by step. ^.^
You got it. I congratulate you on having the perseverance to keep going. You really did the majority of the work here, which is as it should be. You're very welcome for my help. This is the kind of thing I love doing!
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