SOLUTION: Please help me understand how to solve: log(16) 4 I know 4 = (16)^1/2 Help me understand how we get the exponent (1/2). Thanking you in advance.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please help me understand how to solve: log(16) 4 I know 4 = (16)^1/2 Help me understand how we get the exponent (1/2). Thanking you in advance.      Log On


   

Question 766575: Please help me understand how to solve:
log(16) 4
I know 4 = (16)^1/2
Help me understand how we get the exponent (1/2). Thanking you in advance.
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
log(16) 4
I know 4 = (16)^1/2
------------
log%2816%2C4%29
= log%2816%2C16%5E0.5%29
= 1/2

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Learn how to convert a logarithm equation 
into and from an exponential equation. 
That is:

logBA = C is equivalent to BC = A

---------------------------------------------------------

Let x = the answer.  Then

log164 = x, which is equivalent to:

16x = 4

Write 16 as (24) and write 4 as 22

(24)x = 22

Remove the parentheses by multiplying the exponents:

 24x = 22

When there is one exponential on both sides with the 
same base, and that base is positive and not equal to 1,
then we may set the exponents equal to each other:

 4x = 2
  x = 2%2F4
  x = 1%2F2

Edwin