Question

Find the solution to the equation log16 32 = x + 3

Answer 1

Log base 16 if 32 = (x + 3) means, by definition of logarithms that:

16 ^(x+3) = 32

Answer 2

Rewrite 16 as a power of 2.
Do the same for 32.

Answer 3

2^4 = 16
2^5 = 32
The purpose of rewriting 16 and 32 as powers of 2 is to apply exponential properties in the solution process.

Answer 4

16 ^(x+3) = 32

(2^4)^(x+3) = 2^5

2^4(x+3) = 2^5

So, 4(x+3) = 5

Solve 4(x+3) = 5 and check to see if the resulting value of x works in the original equation.

I will draw most of the solution by hand so that it will make more sense.