How do you condense #ln 3 − 2 ln 5 + ln 10#?

2 Answers
EZ as pi
Jun 28, 2016

#ln( 30/25)#

Explanation:

Adding logs means you were multiplying the numbers and dividing numbers means you were dividing the numbers.

#ln3 - 2ln5 + ln10 rArr ln3 - ln5^2 + ln10#

=#ln[(3xx10)/5^2]#

=#ln (30/25)#

Jim G.
Jun 28, 2016

#ln(6/5)#

Explanation:

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

#•lnx+lny=ln(xy)........ (1)#

#•lnx-lny=ln(x/y)........ (2)#

#•lnx^nhArrnlnx........ (3)#

These laws may be used on logarithms to any base.

Using (1) :#ln3+ln10=ln(3xx10)=ln30#

Using (3): #2ln5=ln5^2=ln25#

Using (2):# ln30-ln25=ln(30/25)=ln(6/5)#

#rArrln3-2ln5+ln10=ln(6/5)#

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