Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Test: 23

Answer

{$\frac{43}{21}$}

Work Step by Step

Step 1: $\log_{4} (x+1)-\log_{4} (x-2)=3$ Step 2: $\log_{4} (\frac{x+1}{x-2})=3$ Step 3: $(\frac{x+1}{x-2})=4^{3}$ Step 4: $(\frac{x+1}{x-2})=64$ Step 5: $x+1=64(x-2)$ Step 6: $x+1=64x-128$ Step 7: $64x-128=x+1$ Step 8: $64x-x=1+128$ Step 9: $63x=129$ Step 10: $x=\frac{129}{63}=\frac{43}{21}$ Step 11: Therefore, the solution set is {$\frac{43}{21}$}.
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