Answer:
k = [tex]\frac{25}{12}[/tex]
Step-by-step explanation:
Using the rules of logarithms
log x - log y = log([tex]\frac{x}{y}[/tex] )
log a = log b ⇒ a = b
Given
logk - log(k - 2) = log25, then
log ([tex]\frac{k}{k-2}[/tex] ) = log25, thus
[tex]\frac{k}{k-2}[/tex] = 25 ( multiply both sides by (k - 2)
25(k - 2) = k
25k - 50 = k ( subtract k from both sides )
24k - 50 = 0 ( add 50 to both sides )
24k = 50 ( divide both sides by 24 )
k = [tex]\frac{50}{24}[/tex] = [tex]\frac{25}{12}[/tex]
