What is 2ln(x+4)-8ln(x) ?

The solution to 2ln(x+4)-8ln(x) is ln(((x+4)^2)/(x^8))

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simplify 2ln(x+4)-8ln(x)

simplify

2 ln (x + 4) - 8 ln (x)

ln (\frac{( x + 4 ) ^{2}}{x ^{8}})

Solution steps

2 ln (x + 4) - 8 ln (x)

Apply log rule:

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

2 ln (x + 4) = ln ((x + 4)^{2})

= ln ((x + 4)^{2}) - 8 ln (x)

Apply log rule:

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

8 ln (x) = ln (x^{8})

= ln ((x + 4)^{2}) - ln (x^{8})

Apply log rule:

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

ln ((x + 4)^{2}) - ln (x^{8}) = ln (\frac{( x + 4 ) ^{2}}{x ^{8}})

= ln (\frac{( x + 4 ) ^{2}}{x ^{8}})

- lo g_{10} (6.3 \cdot 1 0^{- 6})

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

\frac{ln ( 2 )}{5 ln ( 2 ) - ln ( 7 )}

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

lo g_{3} (4) - lo g_{3} (7)

What is 2ln(x+4)-8ln(x) ?
The solution to 2ln(x+4)-8ln(x) is ln(((x+4)^2)/(x^8))