What is ln(11x)-(5ln(x)+4ln(3y)) ?

The solution to ln(11x)-(5ln(x)+4ln(3y)) is ln((11)/(81x^4y^4))

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simplify ln(11x)-(5ln(x)+4ln(3y))

simplify

ln (11 x) - (5 ln (x) + 4 ln (3 y))

ln (\frac{11}{81 x ^{4} y ^{4}})

Solution steps

ln (11 x) - (5 ln (x) + 4 ln (3 y))

Apply log rule:

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

5 ln (x) = ln (x^{5})

= ln (11 x) - (ln (x^{5}) + 4 ln (3 y))

Apply log rule:

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

4 ln (3 y) = ln ((3 y)^{4})

= ln (11 x) - (ln (x^{5}) + ln ((3 y)^{4}))

Apply log rule:

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

ln (x^{5}) + ln ((3 y)^{4}) = ln (x^{5} (3 y)^{4})

= ln (11 x) - ln (x^{5} (3 y)^{4})

Simplify

x^{5} (3 y)^{4} : 81 x^{5} y^{4}

= ln (11 x) - ln (81 x^{5} y^{4})

Apply log rule:

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

ln (11 x) - ln (81 x^{5} y^{4}) = ln (\frac{11 x}{81 x ^{5} y ^{4}})

= ln (\frac{11 x}{81 x ^{5} y ^{4}})

Cancel the common factor:

x

= ln (\frac{11}{81 x ^{4} y ^{4}})

ln (\frac{1.148}{2.87})

\frac{e ln ( 90 ) + ln ( 6 )}{ln ( 3 ) + ln ( 20 )}

lo g_{b} (\frac{a b ^{3}}{c})

2 ln (a) - ln (2 b) + 2 ln (2)

ln (\frac{27 a}{b})

What is ln(11x)-(5ln(x)+4ln(3y)) ?
The solution to ln(11x)-(5ln(x)+4ln(3y)) is ln((11)/(81x^4y^4))