What is ln(1)-ln(2x) ?

The solution to ln(1)-ln(2x) is -ln(x)-ln(2)

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simplify ln(1)-ln(2x)

simplify

ln (1) - ln (2 x)

- ln (x) - ln (2)

Solution steps

ln (1) - ln (2 x)

Apply log rule:

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

ln (2 x) = ln (2) + ln (x)

= ln (1) - (ln (x) + ln (2))

Apply log rule:

lo g_{a} (1) = 0

= 0 - (ln (x) + ln (2))

0 - (ln (2) + ln (x)) = - (ln (2) + ln (x))

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

Distribute parentheses

= - (ln (x)) - (ln (2))

Apply minus-plus rules

+ (- a) = - a

= - ln (x) - ln (2)

lo g_{10} (2 \cdot 1 0^{- 4})

t x (ln (t x) - ln (t y) - 1)

ln (x) + ln (\frac{y}{x} + 4)

lo g_{10} (191.7 x^{432})

lo g_{10} (x (x - 1)^{2})