What is x if (x^1/3)^(logx x^2 +2)=2log3 27?

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We have to find x if (x^1/3)^(logx x^2 +2)=2log3 27

(x^1/3)^(log(x) x^2 +2) =...

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giorgiana1976 | Student

We'll start by multiplying the exponents of th term from the left side:

(x)^[(logx x^2 +2)/3]=2log3 27

We'll use the power property of logarithms:

(x)^[(2logx x +2)/3]=2log3 27

(x)^[(2 +2)/3]=2log3 27

We'll write 27 as a power of 3:

(x)^(4/3)=2log3 (3^3)

(x)^(4/3)=2*3*log3 (3)

(x)^(4/3)=6

We'll raise the terms both sides to the power 3/4:

x = 6^(3/4)

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