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Use the change of base formula to approximate the solution to log0.5 15=1-2x

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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.

User Gondim
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