Solve for x the equation logx (8e^3) = 2
Given the logarithm equation:
log(x) 8e^3 = 2
We need to find the values of x.
let us rewrite into the exponent form.
==> x^2 = 8e^3
But we know that 8= 2^3
==> x^2 = (2^3)(e^3)
Now we will rewrite as one power.
We know that a^x * b^x = (ab)^x
==> x^2 = (2e)^3
Now we will square both sides.
==> x = sqrt(2e)^3 = 2e*sqrt(2e) = (2e)^3/2
(The answer is written into 3 different forms)
We have log(x) (8e^3) = 2 and we have to find x.
Now log(x) (8e^3) = 2
=> log(x) (2e)^3 = 2
take the antilog of both the sides
=> (2e)^3 = x^2
=> x = ((2e)^3)^(1/2)
=> x = (2e)^(3/2)
Therefore x is equal to (2e)^(3/2).