Solve (t-1)^4/3=4 where t is a real number. Simplify your answer as much as possible. If there is more than one solution separate them with commas.

Question

Solve (t-1)^4/3=4 where t is a real number. Simplify your answer as much as possible. If there is more than one solution separate them with commas.

Answer 1

To solve this equation, you'll first need to move that exponent. You can get rid of it by raising each side to that exponent's reciprocal, 3/4:

 

((t-1)^4/3)^3/4 = 4^3/4

 

Remember that (xⁿ)^m = x^nm, so we have:

 

(t-1)^(4/3)(3/4) = 4^3/4

(t-1)^12/12 = 4^3/4

(t-1)¹ = 4^3/4

t - 1 = 4^3/4

 

Now add 1 to both sides to get an expression for t:

 

t = 4^3/4 + 1

 

Depending on the problem's meaning of "simplify your answer as much as possible," you may be done there or you may want to write it like this:

 

t = (4³)^1/4 + 1

t = 64^1/4 + 1

 

Or, more accurately, like this:

 

t = ±⁴√(64) + 1

t = ±⁴√(2⁶) + 1

t = ±2(⁴√(2²)) + 1

t = ±2(⁴√4) + 1

 

t = 2(⁴√4) + 1, -2(⁴√4) + 1