Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 4 - Review - Exercises: 72

Answer

$$x \approx 2.602452$$

Work Step by Step

$Use$ $a$ $calculator$ $to$ $find$ $the$ $solution$ $of$ $the$ $equation,$ $rounded$ $to$ $six$ $decimal$ $places:$ $2^{3x-5} = 7$ Write the equation in logarithmic form: $b^c = a \rightarrow \log_b a = c$ $2^{3x-5} = 7 \rightarrow \log_2 7 = 3x-5$ $$\log_2 7 = 3x-5$$ Solve for x add 5 to both sides $$5+\log_2 7 = 3x-5+5$$ $$5+\log_2 7 = 3x$$ Divide both sides by 3 $$\frac{5+\log_2 7}{3} = \frac{3x}{3}$$ $$x = \frac{5+\log_2 7}{3}$$ Plug into calculator $$x = 2.602451640685868$$ Round to six decimal places $$x \approx 2.602452$$
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