danitita18122002 danitita18122002
  • 17-11-2018
  • Mathematics
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How can I make this exercise?? Please Help

How can I make this exercise Please Help class=

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jimrgrant1 jimrgrant1
  • 17-11-2018

x = 3 or x = 1

note that log 5 is usually taken to mean [tex]log_{10}[/tex] 5

using the law of logarithms

logx - logy = log ([tex]\frac{x}{y}[/tex])

the right hand side can be expressed as

log 10000 - log 16 = log ([tex]\frac{10000}{16}[/tex]) = log 625

divide both sides by log 5

x² - 4x + 7 = [tex]\frac{log625}{log5}[/tex] = 4

subtract 4 from both sides

x² - 4x + 3 = 0 ← in standard form

(x - 3 )(x - 1) = 0

equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 1 = 0 ⇒ x = 1


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