Part 1: Find the solution to the equation log16 32 = x + 3. (4 points)

Part 2: Using complete sentences, explain the procedure used to solve this equation. (4 points)

Question

Part 1: Find the solution to the equation log16 32 = x + 3. (4 points) 

Part 2: Using complete sentences, explain the procedure used to solve this equation. (4 points)

campbell_st · Answer

ok... you need to use the log law which is 

$$a^{\log{a}(b)} = b$$

so if you raise each side as a power of 16 you will have 

$$32 = 16^{x + 3}$$

next you need to write 32 and 16 in terms of powers of 2

so you have 

$$2^5 = (2^4)^{x + 3}$$

use the power of a power and you get

$$2^5 = 2^{4x + 12}$$

so all you need to do is solve

5 = 4x + 12 

to find the value of x