SOLUTION: Can you solve for x: 9 to the x power equals 3? x solve for x: 9 = 3

Question 29255: Can you solve for x: 9 to the x power equals 3?

x
solve for x: 9 = 3

Found 2 solutions by sdmmadam@yahoo.com, Nate:
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
9 to the x power equals 3?
(9)^x = 3
[(3^2)]^x = 3
That is (3)^(2x) = (3)^1
implies (2x) = 1 (using (a)^m = (a)^n implies m = n)
x= (1/2)
Answer:x=(1/2)
Verification: (9)^x =(9)^(1/2) = 3 correct
Note: Why should we write 9 as (3^2)?
We write it so because the quantity on the other side is 3 which means
it is (3)^1 and so we try to write the LHS and the RHS in terms of the same base so that we can apply the rule:
bases are the same and so the powers are equal
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
9^x=3
is the same as
x log9=log3 (divide by log9)
x=log3/log9=.5

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