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
