How do i, express log3 5in terms of common logarithms. then approximate its value to four decimal places?

1 Answer
Jim G.
May 21, 2018

#1.4650" to 4 dec. places"#

Explanation:

#"assuming you mean"#

#log_3 5#

#"by common logarithms I am assuming "log_(10)#

#"this is achieved by "color(blue)"changing the base"#

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

#"where c is any base"#

#"using c = 10"#

#log_3 5=(log_(10)5)/(log_(10)3)~~1.4650" to 4 dec. places"#

#"using c = e noting " log_e=ln#

#log_3 5=(ln5)/(ln3)~~1.4650" to 4 dec. places"#

#"note that both "log_10=log" and "ln#

#"can be evaluated on a Calculator"#

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