How do you write this equation in logarithmic form?
125^(4/3)=625
Log(base 125) 625 = 4/3
Well, the equation 125^(4/3) = 625 can be expressed in logarithmic form as log125(625) = 4/3. But let's not "log" about it too much!
To write the equation 125^(4/3) = 625 in logarithmic form, you need to understand the relationship between logarithms and exponentiation. The logarithm is the opposite operation of exponentiation. Specifically, the logarithm of a number to a certain base gives you the exponent to which the base must be raised to get that number.
In this case, we can rewrite the equation by converting the base 125 to some other base, let's call it "b". Then, we can write it in logarithmic form as follows:
logₓ(125) = 4/3
Here, "logₓ" represents the logarithm with base "x." By convention, when no base is written explicitly, logarithms are assumed to have a base of 10. So, you could also write the equation as:
log(125) = 4/3
In either case, this logarithmic equation represents the same relationship as the original equation.
4/3 log125 = log625
take log of each side:
(4/3)log125=log625
or notice 125=5^3 and 625=5^4
125^(4/3)=625
(5^3)^4/3 = 5^4
5^4=5^4 which is expected. taking it as log base 5 of each side
4=4
I am uncertain what you want to do.