Question

Find the value of k given that logk - log (k-2) = log5

Answer 1

4k = 10

k = \frac{10}{4}

= \frac{5}{2}

Answer 2

k = $\frac{5}{2}$

using the ' laws of logarithms '

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

logx = logy ↔ x = y

logk - log(k - 2) = log5

log ( $\frac{k}{(k - 2)}$ =log 5

$\frac{k}{(k - 2)}$ = 5

5(k - 2) = k

5k - 10 = k

4k = 10 ⇒ k = $\frac{10}{4}$ = $\frac{5}{2}$