# Thread: Solving an exponential equation.

1. ## Solving an exponential equation.

$[(2x^1^/^3)-(5^1^/^3)]^3 = 35$

find X ???

2. ## Re: i want help with finding solution set of exponential equation

Originally Posted by mido22
$[(2x^1^/^3)-(5^1^/^3)]^3 = 35$

find X ???
You can treat this like a normal equation to isolate 2x^(1/3):
$2x^{1/3} = \sqrt[3]{35} + 5^{1/3}$

3. ## Re: i want help with finding solution set of exponential equation

sorry but this is not the right solution in my book....
here is the main problem :
$(2x^1^/^3 - 5^1^/^3) (4x^2^/^3 + 2(5x)^1^/^3 + 25^1^/^3) = 35$

then i tried to simplify it as i wrote in the 1st post

the solution set is {5}

4. ## Re: i want help with finding solution set of exponential equation

Originally Posted by mido22
sorry but this is not the right solution in my book....
Always state the problem in full, we can only answer what's put in front of us

here is the main problem :
$(2x^1^/^3 - 5^1^/^3) (4x^2^/^3 + 2(5x)^1^/^3 + 25^1^/^3) = 35$

then i tried to simplify it as i wrote in the 1st post

the solution set is {5}
Start by expanding the brackets:

Multiplying $2x^{1/3}$ by each term in the second bracket:

$8x + 4\sqrt[3]{5}x^{2/3} + 2\sqrt[3]{25}x^{1/3}$

Multiplying $-5^{1/3}$ by each term in the second bracket

$-4\sqrt[3]{5}x^{2/3} - 2\sqrt[3]{25}x^{1/3} - 5$

The expanded form is the sum of these:

$\left(8x + 4\sqrt[3]{5}x^{2/3} + 2\sqrt[3]{25}x^{1/3}\right)$

$+ \left(-4\sqrt[3]{5}x^{2/3} - 2\sqrt[3]{25}x^{1/3} - 5\right) = 35$

Can you go from there? I expect a few terms will cancel

5. ## Re: i want help with finding solution set of exponential equation

Originally Posted by e^(i*pi)
Always state the problem in full, we can only answer what's put in front of us

Start by expanding the brackets:

Multiplying $2x^{1/3}$ by each term in the second bracket:

$8x + 4\sqrt[3]{5}x^{2/3} + 2\sqrt[3]{25}x^{1/3}$

Multiplying $-5^{1/3}$ by each term in the second bracket

$-4\sqrt[3]{5}x^{2/3} - 2\sqrt[3]{25}x^{1/3} - 5$

The expanded form is the sum of these:

$\left(8x + 4\sqrt[3]{5}x^{2/3} + 2\sqrt[3]{25}x^{1/3}\right)$

$+ \left(-4\sqrt[3]{5}x^{2/3} - 2\sqrt[3]{25}x^{1/3} - 5\right) = 35$

Can you go from there? I expect a few terms will cancel
thank you vm! ....................................