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so im creating a rollercoaster and i want to connect a log function of log 2 (x-68.4125)+10 to a cosine function or sine function how

so im creating a rollercoaster and i want to connect a log function of log2(x-68.4125)+10 to a cosine function or sine function how do i do that applying derivatives and simultaneous equations because the condition are f'1 =f'2

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