What is ln(x)+ln(y)+ln(w)+6ln(z) ?

The solution to ln(x)+ln(y)+ln(w)+6ln(z) is ln(xywz^6)

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simplify ln(x)+ln(y)+ln(w)+6ln(z)

simplify

ln (x) + ln (y) + ln (w) + 6 ln (z)

ln (x y w z^{6})

Solution steps

ln (x) + ln (y) + ln (w) + 6 ln (z)

Apply log rule:

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

ln (x) + ln (y) = ln (x y)

= ln (x y) + ln (w) + 6 ln (z)

Apply log rule:

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

ln (x y) + ln (w) = ln (x y w)

= ln (x y w) + 6 ln (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

6 ln (z) = ln (z^{6})

= ln (x y w) + ln (z^{6})

Apply log rule:

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

ln (x y w) + ln (z^{6}) = ln (x y w z^{6})

= ln (x y w z^{6})

ln (\frac{e ^{x} + 1}{e ^{x} - 1})

- lo g_{10} (3.9 \cdot 1 0^{- 4})

lo g_{5} (x) - lo g_{5} (x^{9})

\frac{1}{2} (lo g_{7} (a) + lo g_{7} (b))

ln (\frac{139}{7})

What is ln(x)+ln(y)+ln(w)+6ln(z) ?
The solution to ln(x)+ln(y)+ln(w)+6ln(z) is ln(xywz^6)