How do you solve $16^(n-7)+5=24$ ?

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Answer 1 · 2016-09-04T19:30:11

$n = 8.06198$

Isolate the term with the variable.

$16^(n-7) = 19$

19 is clearly not an exact power of 16.
The variable is in the index, so use logs.

$log16^(n-7) = log19$

$(n-7)log16 = log19$

$(n-7) = log19/log16$

$n-7 = 1.06198$

$n = 8.06198$

How do you solve 16^(n-7)+5=2416^(n-7)+5=24?