Question

How can I make this exercise?? Please Help

Answer 1

x = 3 or x = 1

note that log 5 is usually taken to mean $log_{10}$ 5

using the law of logarithms

logx - logy = log ($\frac{x}{y}$)

the right hand side can be expressed as

log 10000 - log 16 = log ($\frac{10000}{16}$) = log 625

divide both sides by log 5

x² - 4x + 7 = $\frac{log625}{log5}$ = 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