how to isolate a variable with a component.
60+80x1 over 2 to the exponent of "T" over 30+20
To isolate a variable in an equation with components, you need to follow a series of steps. Let's break down the given equation and isolate the variable "T":
1. Start with the original equation:
(60 + 80x1) / (2^T) = (30 + 20)
2. Simplify the numerical parts of the equation:
140 / (2^T) = 50
3. To isolate the variable "T," we will first eliminate the fraction by multiplying both sides of the equation by the denominator:
140 = 50 * (2^T)
4. Next, divide both sides of the equation by 50:
140 / 50 = (2^T)
Simplify the left side:
2.8 = (2^T)
5. To isolate the base, take the logarithm (base 2) of both sides of the equation:
log base 2 (2.8) = log base 2 (2^T)
Using the property of logarithms (log base a (a^b) = b), the equation becomes:
log base 2 (2.8) = T
6. Finally, use a calculator or logarithmic tables to find the log base 2 of 2.8, which gives you the value of T.
Therefore, to isolate the variable "T" in the given equation, you need to take the logarithm (base 2) of both sides of the equation using a calculator or logarithmic tables.