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

Question

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

 

 

Please help!

Answer 1

log1632 = x + 2

 

The solution to a logarithm is the exponent.  The base number of a log is 10.

 

 

10^{(x + 2)} = 1632

 

 

Log both sides of the equation and bring the exponent down as the coefficient of the log.

 

(x + 2)log10 = log(1632)

 

 

Divide both sides of equation by log10.

 

x + 2 = 3.21

 

 

Subtract 2 on both sides of equation.

 

x = 1.21