how do you find x for the function: g(x) = 2^3(square root of X)-1
interpretation:
g(x) = 2^(3√x) - 1
"how do you find x for the function" is not a valid question.
did you mean: For what values of x is the function zero ?
yes
To find x for the function g(x) = 2^(3√x) - 1, we need to isolate x on one side of the equation. Here's how you can approach it:
Step 1: Start with the given equation: g(x) = 2^(3√x) - 1.
Step 2: Add 1 to both sides of the equation to isolate the exponentiated term: g(x) + 1 = 2^(3√x).
Step 3: Take the logarithm (base 2) of both sides to remove the exponentiation: log_2(g(x) + 1) = log_2(2^(3√x)).
Step 4: Apply the logarithmic property, which states that log_b(b^a) = a, to the right side of the equation: log_2(g(x) + 1) = 3√x.
Step 5: Raise both sides of the equation to the power of 2 to remove the logarithm and obtain: 2^(log_2(g(x) + 1)) = 2^(3√x).
Step 6: Simplify the left side using the logarithmic property log_b(b^a) = a to get: g(x) + 1 = 2^(3√x).
Step 7: Subtract 1 from both sides of the equation: g(x) = 2^(3√x) - 1.
Now, you have an equation that is equivalent to the original function g(x) = 2^(3√x) - 1. However, it is not possible to obtain a numerical solution for x without more information or a specific value for g(x).