How do you rewrite #log_7.1x# as a ratio of common logs and natural logs?

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Alan P. Share
Jan 11, 2017

Answer:

#log_(7.1)x=color(blue)((log_10 (x))/(log_10 (7.1)))=color(green)((ln(x))/(ln(7.1)))#

Explanation:

The general Change of Base formula is
#color(white)("XXX")log_b a=(log_d(a))/(log_d(b))#

The common log is taken (by most people) to be #log_10#
and
the natural log is #log_e=ln#

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