How do you solve #6*14^k+4=76#?

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Answer 1 · 2016-09-18T16:16:16

#color(darkred)(k) = 0.9416#

As with a normal equation, isolate the term or factor which contains the variable.

#6xxcolor(tomato)(14^k) +4 = 76" "larr# subtract 4 from both sides

#6xxcolor(tomato)(14^k) = 72" "# divide by 6 on both sides

#color(tomato)(14^k) = 12#

12 is clearly not an exact power of 14, so logs are indicated.

#log14^color(darkred)(k) = log12" "larr# apply the log power law

#color(darkred)(k)log14 = log12" "larr# isolate k

#color(darkred)(k) = log12/log14" "larr# use a calculator

#color(darkred)(k) = 0.9416#