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Question
Working with special derivatives, can't get this practice problem (keep getting different answers, none of which match the one provided). Hoping you could help. It is:

Find an equation for a line that is tangent to the graph of y=log(subscript 4) x^(2)    at x=1

Thank you for your time and assistance.

Answer
y = log4(x)^2 = lnx^2/ln4, where ln is the log to base e.
So y = (2lnx)/ln4

dy/dx = 2/(xln4). At x =1 dy/dx = 2/(ln4).
Also at x =1 y = log1 = 0.

y = mx + c, =2x/ln4 + c, but at x = 1, y=0.

0 = 2/ln4 + c, so c = -2/ln4.

Thus equatn. of tangent is y = 2x/ln4 - 2/ln4.

Calculus

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