SOLUTION: Solve and round to the nearest thousandth. 16^(n-7)+5=24

Question 558397: Solve and round to the nearest thousandth.
16^(n-7)+5=24
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
16^(n-7)+5=24
subtract 5 from both sides of the equation to get:
16^(n-7) = 19
take the log of both sides of the equation to get:
log(16^(n-7) = log(19)
this becomes:
(n-7)*log(16) = log(19)
divide both sides of this equation by log(16) to get:
n-7 = log(19)/log(16)
add 7 to both sides of this equation to get:
n = (log(19)/log(16)) + 7
use your calculator to solve for n to get:
n = 8.061981878
replace n in your original equation to confirm.
original equation is:
16^(n-7) + 5 = 24
replace n with 8.061981878 to get:
16^(8.061981878 - 7) + 5 = 24
use your calculator to to get:
24 = 24
this confirms the value of n is good.

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