How do you use the Change of Base Formula and a calculator to evaluate the logarithm #log_5 7#?

3 Answers
Mar 4, 2018

Answer:

#log_5(7)~~1.21#

Explanation:

The change of base formula says that:
#log_alpha(x)=log_beta(x)/log_beta(alpha)#

In this case, I will switch the base from #5# to #e#, since #log_e# (or more commonly #ln#) is present on most calculators. Using the formula, we get:

#log_5(7)=ln(7)/ln(5)#

Plugging this into a calculator, we get:

#log_5(7)~~1.21#

Mar 4, 2018

Answer:

#"Approx. "1.209#.

Explanation:

The Change of Base Formula : #log_ba=log_c a/log_c b#.

#:. log_5 7=log_10 7/log_10 5#,

#=0.8451/0.6990~~1.209#.

Mar 4, 2018

Answer:

#log_5 7~~1.21" to 2 dec. places"#

Explanation:

#"the "color(blue)"change of base formula"# is.

#•color(white)(x)log_b x=(log_c x)/(log_c b)#

#"log to base 10 just log and log to base e just ln"#
#"are both available on a calculator so either will"#
#"give the result"#

#rArrlog_5 7=(log7)/(log5)~~1.21" to 2 dec. places"#

#"you should check using ln"#