Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Review - Exercises: 71

Answer

$$x \approx 0.430618$$

Work Step by Step

$Use$ $a$ $calculator$ $to$ $find$ $the$ $solution$ $of$ $the$ $equation,$ $rounded$ $to$ $six$ $decimal$ $places:$ $$5^{-\frac{2x}{3}} = 0.63$$ Write the exponent form to logarithmic form: $b^c = a \rightarrow \log_b a =c $ $5^{-\frac{2x}{3}} = 0.63 \rightarrow \log_5 0.63 = -\frac{2x}{3}$ $\log_5 0.63 = -\frac{2x}{3}$ Solve for x Multiply both sides by 3 $3(\log_5 0.63) = 3(\frac{2x}{3})$ $3\log_5 0.63 = 2x$ Divide both sides by -2 $\frac{3\log_5 0.63}{-2} = \frac{2x}{-2}$ $$x = \frac{3\log_5 0.63}{-2}$$ Plug into calculator $$x = 0.430618158078972$$ Round to six decimal places $$x \approx 0.430618$$
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