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

$color(darkred)(k) = 0.9416$

How do you solve 6*14^k+4=766*14^k+4=76?