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Popular >

simplify ln(1/3)-ln(x)

Solution

simplify

ln (\frac{1}{3}) - ln (x)

Solution

- ln (3 x)

Solution steps

ln (\frac{1}{3}) - ln (x)

Apply log rule:

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

ln (\frac{1}{3}) - ln (x) = ln (\frac{\frac{1}{3}}{x})

= ln (\frac{\frac{1}{3}}{x})

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= ln (\frac{1}{3 x})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (3 x)

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Frequently Asked Questions (FAQ)

What is ln(1/3)-ln(x) ?
The solution to ln(1/3)-ln(x) is -ln(3x)