Solve for x  the equation logx (8e^3) = 2

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hala718 eNotes educator | Certified Educator

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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)

 

justaguide eNotes educator | Certified Educator

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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).

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