simplify ln(1/x)

Solution

simplify

ln (\frac{1}{x})

- ln (x)

Solution steps

ln (\frac{1}{x})

Apply log rule:

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

ln (\frac{1}{x}) = ln (1) - ln (x)

= ln (1) - ln (x)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (x)

0 - ln (x) = - ln (x)

= - ln (x)

ln (5 e^{6})

- \frac{1}{4} lo g_{2} (\frac{1}{4}) - \frac{3}{4} lo g_{2} (\frac{3}{4})

f (x) = ln (5 e^{x})

f (x) = \frac{1}{7} [lo g_{10} (x) - lo g_{10} (x + 4)]

f (x) = lo g_{6} (1296 x)