how to isolate a variable with a component.
60+80x1 over 2 to the exponent of "T" over 30+20
solve for T
To isolate the variable "T" in the given equation, we can follow these steps:
Step 1: Simplify the expression.
Begin by applying the exponent to the base (2^T). This can be restated as 2 * 2 * 2 * 2 * ... * 2 (T times). So, 2^T equals 2 * 2 * 2 * ... * 2 (T times).
Step 2: Evaluate the expression.
Now, substitute the simplified expression back into the original equation:
(60 + 80x1) / (2^T / 30 + 20)
Step 3: Continue simplifying.
Next, we can simplify the expression further by multiplying both the numerator and denominator by 30 + 20 to remove the fraction:
(60 + 80x1)(30 + 20) / (2^T)
Step 4: Further simplify the expression.
Multiply the terms in the numerator:
(1800 + 1200x1 + 2400 + 1600x1) / (2^T)
Step 5: Combine like terms.
Simplify the numerator:
(4200 + 2800x1) / (2^T)
Step 6: Reorder the expression.
Rearrange the numerator:
(2800x1 + 4200) / (2^T)
Step 7: Rearrange the equation.
Now, rewrite the equation:
(2800 + 4200) / (2^T) = T
Step 8: Further simplify the expression.
Combine like terms in the numerator:
(2800 + 4200) / (2^T) = T
Step 9: Calculate the expression.
Perform the addition in the numerator:
7000 / (2^T) = T
Step 10: Isolate the variable.
To isolate variable 'T', multiply both sides of the equation by (2^T):
7000 = T * (2^T)
At this point, it is not possible to isolate 'T' algebraically. Numeric or iterative methods may be required to solve for 'T'.