Question

use the change of base formula to approximate the solution to \\(\log_{0.5} 15 = 1 - 2x\\). round to the nearest hundredth.

\\(x = \\)

Explanation:

Apply the change of base formula

Using the Change of Base Formula knowledge point

$$ \log_{0.5}15 = \frac{\ln(15)}{\ln(0.5)} $$

Calculate the logarithmic value

Using the Logarithmic Evaluation knowledge point

$$ \log_{0.5}15 \approx \frac{2.70805}{-0.69315} \approx -3.90689 $$

Set up the linear equation

Using the Linear Equations knowledge point

$$ -3.90689 = 1 - 2x $$

Solve for x

Using the Linear Equations knowledge point

$$
LATEXBLOCK0
$$

Round to the nearest hundredth

Using the Algebraic Simplification knowledge point

$$ x \approx 2.45 $$

Answer:

Use the change of base formula to approximate the solution to \(\log_{0.5}15 = 1 - 2x\). Round to the nearest hundredth.

\(x =\) <blank>2.45</blank>