Solving Log Base Homework: 3 = Log2x 64

[Faint]

Homework Statement

3 = Log_2x 64

Homework Equations

N/a

The Attempt at a Solution

3 = Log_2x 64
2x³ = 64
x³ = 32
x = Cubic root of 32
x = 3.1748

I'm fairly certain the answer has to be 2 b/c 2x would be equal to 4, and 4³ = 64.

Anyone mind helping me on this one? Probably a really simple error.

 

[Saladsamurai]

(2x)³ not 2*x³

Hover: your logic is flawed in that it omits the log

 

[Faint]

You got the right answer. Nothing is wrong with it. Whenever you feel that your answer might be wrong, plug it back into the equation and see what you get.

2x^3 = 64
2(3.1748)^3=?
2*31.999=64


2 for an answer is incorrect. To check this, plug it back into the equation.

2x^3 = 64
2(2)^3=?
2^4=16

16 doesn't equal 64

(2x)³ not 2*x³

Hover: your logic is flawed in that it omits the log

As Saladsamurai said, the entire (2x) term would be cubed. The resulting answer is then 256, which is too much obviously.

 

[Saladsamurai]

$(2x)^3=64\Rightarrow 2^3*x^3=64\Rightarrow 8x^3=64\Rightarrow x^3=8\Rightarrow x=2$

We okay now?

 

[Faint]

Yep, understand. Thank you :)