How do you condense #Log2r-2log4p+1/2log16x+2#?

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Answer 1 · 2016-07-26T18:59:20

#log[(50r x^(1/2))/p^2]#

Before we can condense all the terms, they all need to be log terms.
#Log2r-2log4p+1/2log16x+2#?
#2 = log100#
#Log2r-2log4p+1/2log16x+log 100#

Use the power law:

=#Log2r-log(4p)^2+log(16x)^(1/2)+log 100#

If logs are being added or subtracted, the numbers are being multiplied or divided.

= #log [(2r xx (16x)^(1/2) xx 100)/((4p)^2)]#

=#log [(200 r xx 4(x)^(1/2) )/(16p^2)]#

=#log[(50r x^(1/2))/p^2]#