log (x + 16) = log x + log 16

Question

4. Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expression. Give the exact answer.
log (x + 16) = log x + log 16

Answer 1

Hi Jacob;

log (x + 16) = log x + log 16

For the right side of the equation, let's apply the principle...

log ab=log a + log b

log(x+16)=log 16x

Let's remove the logarithms of both sides...

x+16=16x

Let's subtract x from both sides...

x-x+16=16x-x

16=15x

Let's divide both sides by 15...

16/15=(15x)/15

16/15=x

Answer 2

Take inverse natural log for both sides of the equation.

 

e^log(x+16) = e^{(log x + log 16)}

 

Since log ab = log a + log b  , we can apply this to the right side of our equation...

 

e^log(x+16) =  e^{(log 16x)}

 

Since e and log cancel each other out....

 

x+16 = 16x

 

Now solve for x

 

16 = 15x

 

ANSWER: x= 16/15