Question

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

Answer 1

thanks

Answer 2

using the log laws

\[\log(ab) = \log(a) + \log(b)\]

and \[\log _{a} a = 1\]

so look at \[\log _{16} (32) = \log _{16}(2\times16) = \log _{16}(2) + 1\]

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

\[\frac{5}{4} = x + 5\]

solve for x

Answer 3

thank you so much