What is 9/2 ln(60-x)+ln(30-x) ?

The solution to 9/2 ln(60-x)+ln(30-x) is ln((60-x)^{9/2}(30-x))

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simplify 9/2 ln(60-x)+ln(30-x)

simplify

\frac{9}{2} ln (60 - x) + ln (30 - x)

ln ((60 - x)^{\frac{9}{2}} (30 - x))

Solution steps

\frac{9}{2} ln (60 - x) + ln (30 - x)

Apply log rule:

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

\frac{9}{2} ln (- x + 60) = ln ((- x + 60)^{\frac{9}{2}})

= ln ((- x + 60)^{\frac{9}{2}}) + ln (- x + 30)

Apply log rule:

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

ln ((60 - x)^{\frac{9}{2}}) + ln (30 - x) = ln ((- x + 30) (- x + 60)^{\frac{9}{2}})

= ln ((60 - x)^{\frac{9}{2}} (30 - x))

\frac{1}{1} - 5 ln (\frac{6}{5})

lo g_{5} (\frac{y ^{4}}{3 x})

ln (\frac{e ^{- c} ( 1 + c )}{c ^{2}})

lo g_{10} (\frac{z ^{5} y ^{4}}{x ^{5}})

lo g_{2} (x) + 8 lo g_{2} (y)

What is 9/2 ln(60-x)+ln(30-x) ?
The solution to 9/2 ln(60-x)+ln(30-x) is ln((60-x)^{9/2}(30-x))