Given the function #y=log(x), 0<x<10#, what is the slope of the graph where #x=5.7#?

1 Answer
1s2s2p
Dec 20, 2017

#(dy)/(dx)=0.076#

Explanation:

Assuming the log is taken to base 10, then we can use the log rule: #log_b(c)=log_a(c)/log_b(b)#, to change our function to:
#y=ln(x)/ln(10)=1/ln(10)*ln(x)#

#d/(dx)ln(x)=1/x#

#y=aln(x)#

#y'=a*1/x#

By inserting #a=1/ln(10)# we get:

#y'=1/(xln(10))=1/ln(10^x)#

#1/ln(10^5.7)=0.076#

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