What is ((6ln(x+9)+ln(x)-2ln(x)))/2 ?

The solution to ((6ln(x+9)+ln(x)-2ln(x)))/2 is (ln(((x+9)^6)/x))/(2)

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simplify ((6ln(x+9)+ln(x)-2ln(x)))/2

simplify

\frac{( 6 ln ( x + 9 ) + ln ( x ) - 2 ln ( x ) )}{2}

\frac{ln ( \frac{( x + 9 ) ^{6}}{x} )}{2}

Solution steps

\frac{( 6 ln ( x + 9 ) + ln ( x ) - 2 ln ( x ) )}{2}

Apply log rule:

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

6 ln (x + 9) = ln ((x + 9)^{6})

= \frac{( ln ( ( x + 9 ) ^{6} ) + ln ( x ) - 2 ln ( x ) )}{2}

Apply log rule:

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

ln ((x + 9)^{6}) + ln (x) = ln (x (x + 9)^{6})

= \frac{ln ( ( x + 9 ) ^{6} x ) - 2 ln ( x )}{2}

Apply log rule:

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

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

= \frac{ln ( x ( x + 9 ) ^{6} ) - ln ( x ^{2} )}{2}

Apply log rule:

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

ln (x (x + 9)^{6}) - ln (x^{2}) = ln (\frac{x ( x + 9 ) ^{6}}{x ^{2}})

= \frac{ln ( \frac{( x + 9 ) ^{6} x}{x ^{2}} )}{2}

Cancel the common factor:

x

= \frac{ln ( \frac{( x + 9 ) ^{6}}{x} )}{2}

ln (\frac{3 z + 2 i}{4 z - 5 i})

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

ln (\frac{77 \cdot 914555 - 77}{914555 - 77})

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

ln (15) - 2 (ln (4) + ln (32))

What is ((6ln(x+9)+ln(x)-2ln(x)))/2 ?
The solution to ((6ln(x+9)+ln(x)-2ln(x)))/2 is (ln(((x+9)^6)/x))/(2)