Log a (b)=c is equivalent to a^b=c

Question

True or false with explanation please. Logarithms are so confusing

Answer 1

As Arturo said...

 

If  log_ab = c  then a^c = b

This also means that to convert an exponent expression to a log:

If a^c = b  then  log_ab = c

 

When looking at   log_ab  think of it as asking

"To what power do I raise a to get b?"

 

So:  log_ab = c  means  that c is the power to which a is raised to get b

       so   a^c = b

 

Given your question the answer is FALSE because

log_ab = c is equivalent to a^c = b  NOT  a^b = c

Answer 2

FALSE.

 

If log_ab = c, then by the definition of logarithm,

 

a^c = b