Final answer:
To solve log0.5 15 = 1 - 2x, apply the change of base formula, use natural logarithms to rewrite it, compute the natural logarithms, and then solve algebraically for x.
Step-by-step explanation:
To solve the equation log0.5 15 = 1 - 2x using the change of base formula, we first convert the logarithm to a common base such as base 10 or natural logarithm (ln). The change of base formula states that logb a = logc a / logc b, where c is the new base we are using.
Using the natural logarithm, we can rewrite our equation as:
ln(15) / ln(0.5) = 1 - 2x
To find the value of x, we must first compute the natural logarithms. Once we have that, we can solve for x algebraically:
ln(15) / ln(0.5) = 1 - 2x
(ln(15) / ln(0.5)) + 2x = 1
2x = 1 - (ln(15) / ln(0.5))
x = (1 - (ln(15) / ln(0.5))) / 2
Now substitute the known quantities into the equation and solve for the approximate value of x.