If log(15) + log(y) = log(z), then 15 + y=z?

Question

A) If log(15) + log(y) = log(z), then 15 + y=z

True or False?

B)If ln(15x) = ln (y), then 15x = y.

True or False?

 

For both parts I think its true because it looks like it, but I have no idea. What is the question asking, what rules are we supposed to know to apply. Please correct me if I am wrong and tell me why, because I am a little confused.

 

Answer 1

You are supposed to know the laws of logarithms. They should be printed in your textbook all in one place.

 

A)

log 15 + log y

log 15y

log 15y = log z

15y = z

False

 

B)

ln 15x = ln y

15x = y

True

Answer 2

Part A is false.

log(15)+log(y)=log(z)

e^(log(15)+log(y))=e^(log(z))

e^(log(15)).e^(log(y))=e^(log(z))

15.y=z

 

Part B is true.

ln(15x)=ln(y)

e^(ln(15x))=e^(ln(y))

15x=y