How do you simplify #\log_{5} ( b^{2} a^{8} )#?

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Answer 1 · 2016-10-07T22:33:04

Please follow the instructions below...

Because of logarithmic rules, which can be seen on this page http://mathsvideos.net/log-formulas/, what you see below is true.

#log_5(b^2a^8)#

#=log_5((ba^4)^2)#

#=2log_5(ba^4)#

#=2{log_5(b)+log_5(a^4)}#

#=2{log_5(b)+4log_5(a)}#

#=2log_5(b)+8log_5(a)#

You can find out why the above transformations are mathematically coherent by accessing this playlist: https://www.youtube.com/playlist?list=PLFM03zQeSz2PvB2IxWqcLcZMSIIpcIVtV