Differentiating Logarithmic Functions without Base e
Key Questions
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By Change of Base Formula:
#log_bx={log_ax}/{log_ab}# ,#y=log_3x={lnx}/{ln3}# By taking the derivative,
#y'={1/x}/{ln3}=1/{(ln3)x}# 
Wataru
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4
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Sep 22 2014
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Answer:
#-tan(x)/ln(2)# Explanation:
#f(x)=log_2(cos(x))=ln(cos(x))/ln(2)# #1/ln(2)# is just a constant and can be ignored.#(ln(u))'=(u')/u# #u=cos(x), u'=-sin(x)# #f'(x)=1/ln(2)*(-sin(x))/cos(x)=-tan(x)/ln(2)# 
Martin C.
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1
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Mar 18 2018
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Change of Base Formula
#log_bx={log_ax}/{log_ab}# ,where
#a# is any positive number except#1# .I hope that this was helpful.
Wataru
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Oct 16 2014