Question

Log k-log(k-2)=log25

Answer 1

Answer:

k = $\frac{25}{12}$

Step-by-step explanation:

Using the rules of logarithms

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

log a = log b ⇒ a = b

Given

logk - log(k - 2) = log25, then

log ($\frac{k}{k-2}$ ) = log25, thus

$\frac{k}{k-2}$ = 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 = $\frac{50}{24}$ = $\frac{25}{12}$