Question 1090060: Hello, I'd like to know how to solve the following Logarithmic
equation for x
log125(1/5) = x
I ended up doing this= 5·5^3x=5^1/2
But it does not match with the solution I got on the calculator which is -6.
Thanks for your time. Found 3 solutions by Edwin McCravy, Alan3354, MathTherapy:Answer by Edwin McCravy(20060) (Show Source):
ANY logarithmic equation logB(A) = C
is equivalent to the exponential equation A = BC.
Therefore your logarithmic equation is equivalent to
the exponential equation
Next we write 1/5 as 5-1 and 125 as (53)
We multiply the exponents on the right to remove the
parentheses:
Now Since the bases of the exponents on the laft and right are
equal, positive, and different from 1, the exponents must also
be equal, so we can drop the bases and set the exponents equal:
Divide both sides by 3
Edwin
