What is simplify-ln(((1))/((2y)^3)) ?

The solution to simplify-ln(((1))/((2y)^3)) is 3ln(2y)

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simplify-ln(((1))/((2y)^3))

simplify

- ln (\frac{( 1 )}{( 2 y ) ^{3}})

3 ln (2 y)

Solution steps

- ln (\frac{( 1 )}{( 2 y ) ^{3}})

Apply log rule:

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

ln (\frac{( 1 )}{( 2 y ) ^{3}}) = ln ((1)) - ln ((2 y)^{3})

= - (- ln ((2 y)^{3}) + ln ((1)))

Remove parentheses:

(a) = a

= - (ln (1) - ln ((2 y)^{3}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((2 y)^{3}) = 3 ln (2 y)

= - (ln (1) - 3 ln (2 y))

Apply log rule:

lo g_{a} (1) = 0

= - (- 3 ln (2 y) + 0)

Refine

= 3 ln (2 y)

4 lo g_{2} (m) + 5 lo g_{2} (n)

- lo g_{10} (2.5 \cdot 1 0^{- 13})

ln (\frac{e ^{3 x}}{2})

3 lo g_{6} (x) - lo g_{6} (y)

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

What is simplify-ln(((1))/((2y)^3)) ?
The solution to simplify-ln(((1))/((2y)^3)) is 3ln(2y)