How do you solve #428^-x = 37.5#?

1 Answer
seol
Nov 20, 2016

#x\approx-0.5981626...#

Explanation:

#\color(indianred)(a^x=b)\leftrightarrow\color(olive)(\log_(a)(b)=x)#

input in values:
#\color(indianred)(428^(-x)=37.5)\leftrightarrow\color(olive) (\log_428(37.5)=-x)#
divide both sides by -1 to isolate #x#:
#\log_428(37.5)/\color(red)(-1)=(\cancel(-)x)/\cancel(\color(red)(-1))#
#-\log_428(37.5)=x#

#x\approx-0.5981626...#

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