solve for x:
x^(2/3)=(1/27)
(2^(x)+4)/(2^x)=2
explain please
For the first one, remember that (a^b)^c = a^(bc). 2/3 * 3/2 = 1, so raise each side to the power of 3/2. That's all you need to do; you'll be left with x=(something).
For the second, start by splitting the left side into two fractions, like so:
(2^x)/(2^x) + 4/(2^x) = 2.
(2^x)/(2^x) = 1, so we can subtract that from both sides:
4/(2^x) = 1.
Multiply by 2^x to get that to itself:
4 = 2^x.
And you should be able to finish it yourself.
To solve the equation `x^(2/3) = (1/27)`, you need to isolate the variable `x`. Here's how you can do that:
Step 1: Simplify both sides of the equation by taking the cube root of both sides:
(x^(2/3))^(3) = (1/27)^(3/1)
x^(2/3 * 3) = 1/27
x^2 = 1/27
Step 2: Take the square root of both sides to eliminate the exponent:
√(x^2) = √(1/27)
x = ±√(1/27)
Step 3: Simplify the expression on the right side:
x = ±√(1)/√(27)
x = ±(1/3√3)
Therefore, the solutions to the equation `x^(2/3) = (1/27)` are x = (1/3√3) and x = -(1/3√3).
Moving on to the next equation `((2^x) + 4)/(2^x) = 2`, follow these steps to solve for `x`:
Step 1: Multiply both sides of the equation by `2^x` to eliminate the fraction:
(2^x)((2^x) + 4)/(2^x) = 2 * (2^x)
(2^x) + 4 = 2 * (2^x)
Step 2: Expand the equation:
2^x + 4 = 2^x * 2
Step 3: Subtract 2^x from both sides of the equation:
2^x + 4 - 2^x = 2^x * 2 - 2^x
4 = 2^x * 2 - 2^x
Step 4: Simplify:
4 = 2 * 2^x - 2^x
4 = 2 * 2^x - 1 * 2^x
4 = (2 - 1) * 2^x
4 = 2^x
Step 5: Rewrite `4` as `2^2`:
2^2 = 2^x
Step 6: Since the base is the same (2), equate the exponents:
2 = x
Therefore, the solution to the equation `((2^x) + 4)/(2^x) = 2` is x = 2.