Question

Find the solution to the equation log16 32 = x + 5. Using complete sentences, explain the procedure used to solve this equation.

Answer 1

Use the log laws.
\[\log(ab)=\log(a)+\log(b)\] and
\[\log _{a} a=1\]
so look at
\[\log _{16}(32)=\log _{16}(2 \times 16)=\log _{16}(2)+1\]
and \[2=16^{1/4}\]
so \[\log _{16}(16\frac{ 1 }{ 4 })=1/4\]
So the problem is now \[\frac{ 1 }{ 4 }+1=x +5 \] or, \[\frac{ 5 }{ 4 }=x +5\]
Now Solve for x!

Answer 2

would it be x=-15/4?

Answer 3

Yep!!:)

Answer 4

awesome! thank you!! :D

Answer 5

No problem!!:) Anytime!!!:)