simplify ln((8x)/y)

Solution

simplify

ln (\frac{8 x}{y})

3 ln (2) + ln (x) - ln (y)

Solution steps

ln (\frac{8 x}{y})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{8 x}{y}) = ln (8 x) - ln (y)

= ln (8 x) - ln (y)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (8 x) = ln (8) + ln (x)

= ln (8) + ln (x) - ln (y)

ln (8) = 3 ln (2)

= 3 ln (2) + ln (x) - ln (y)

lo g_{5} (h - 1) + lo g_{5} (h + 3)

lo g_{2} (x lo g_{5} (x))

lo g_{b} (\frac{15}{2})

lo g_{2} (\frac{1}{0.1}) - 1