X to the 4/3 power minus 5 equals 11

X^4/3 - 5 = 11
X^(4/3) = 16

Take the logarithm of both sides and simplify. Once you get it into the form

Log(x) = something

Take the antilog (10 to the power) and you have your answer.

You can also use the natural log instead of the common log, if you wish.

Hint: Answer is between 1 and 20

Much easier approach:


x^{4/3} = 16 \\


Cube both sides:

(x^{4/3})^3 = 16^3 \\


Recall that ({x^a})^b = x^{ab}, hence

(x^{4/3})^3 = x^4


So you have:

x^4 = 16^3


Can you take it from here?