What is ln^5(+1ln(y)-7ln(x)) ?

The solution to ln^5(+1ln(y)-7ln(x)) is ln^5(ln(y/(x^7)))

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simplify ln^5(+1ln(y)-7ln(x))

simplify

ln^{5} (+ 1 ln (y) - 7 ln (x))

ln^{5} (ln (\frac{y}{x ^{7}}))

Solution steps

ln^{5} (1 \cdot ln (y) - 7 ln (x))

Apply log rule:

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

1 \cdot ln (y) = ln (y^{1})

= ln^{5} (ln (y^{1}) - 7 ln (x))

Apply log rule:

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

7 ln (x) = ln (x^{7})

= ln^{5} (ln (y^{1}) - ln (x^{7}))

Apply log rule:

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

ln (y^{1}) - ln (x^{7}) = ln (\frac{y ^{1}}{x ^{7}})

= ln^{5} (ln (\frac{y ^{1}}{x ^{7}}))

Apply rule

a^{1} = a

y^{1} = y

= ln^{5} (ln (\frac{y}{x ^{7}}))

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

- 6 ln (2 y)

lo g_{2} (\frac{5}{200})

8 x^{3} + 3 ln (2 x) + 3 e^{x} + 6

\frac{1}{4 - 2} ln (\frac{4}{2})

What is ln^5(+1ln(y)-7ln(x)) ?
The solution to ln^5(+1ln(y)-7ln(x)) is ln^5(ln(y/(x^7)))