Question

Find the solution to the equation log16 32 = x + 2. Using complete sentences, explain the procedure used to solve this equation.

Answer 1

IS it Log base 16 of 32?

Answer 2

yes. log base 16 of 32 = x + 2

Answer 3

If it is : \[\log_{16} 32 = \log_{16}(16\times2)=\log_{16}16 + \log_{16}2 = 1 + [\log_{2}2/\log_{2}16] = 1 + 1 / [4\log_{2}2] \]

Answer 4

\[1 + 1/[4\log_{2}2] = 1 + 1/4 = 5/4 \]

Answer 5

So know you have 5 / 4 = x+ 2
5 = 4x + 8
4x = -3
x = -3/4

Answer 6

The main part of this question is using property of logs to simplify the left side of the equation to 5/4