How do you simplify #ln 3 − 2 ln 8 + ln 16#?

2 Answers
Alex C.
Mar 25, 2018

#ln(3/4)#

Explanation:

We have to use the Logarithm Properties.

#ln(3)-2ln(8)+ln(16)#

We can rewrite the initial expression using the Power rule in this way
#ln(3)-ln(8^2)+ln(16)#

#ln(3)-ln(64)+ln(16)#

Here we use the Quotient rule
#ln(3/64)+ln(16)#

And here the Product rule
#ln(3/64*16)#

#ln(48/64)#

Finally we get the semplified version :
#ln(3/4)#

Jim G.
Mar 25, 2018

#ln(3/4)#

Explanation:

#"using the "color(blue)"laws of logarithms"#

#•color(white)(x)logx^nhArrnlogx#

#•color(white)(x)logx+logyhArrlog(xy)#

#•color(white)(x)logx-logyhArrlog(x/y)#

#rArrln3-ln8^2+ln16#

#=ln((3xx16)/64)=ln(48/64)=ln(3/4)#

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