What is 9/10 ln(2x+4)-12/5 ln(x+3) ?

The solution to 9/10 ln(2x+4)-12/5 ln(x+3) is ln(((2x+4)^{9/10})/((x+3)^{12/5)})

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simplify 9/10 ln(2x+4)-12/5 ln(x+3)

simplify

\frac{9}{10} ln (2 x + 4) - \frac{12}{5} ln (x + 3)

ln (\frac{( 2 x + 4 ) ^{\frac{9}{10}}}{( x + 3 ) ^{\frac{12}{5}}})

Solution steps

\frac{9}{10} ln (2 x + 4) - \frac{12}{5} ln (x + 3)

Apply log rule:

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

\frac{9}{10} ln (2 x + 4) = ln ((2 x + 4)^{\frac{9}{10}})

= ln ((2 x + 4)^{\frac{9}{10}}) - \frac{12}{5} ln (x + 3)

Apply log rule:

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

\frac{12}{5} ln (x + 3) = ln ((x + 3)^{\frac{12}{5}})

= ln ((2 x + 4)^{\frac{9}{10}}) - ln ((x + 3)^{\frac{12}{5}})

Apply log rule:

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

ln ((2 x + 4)^{\frac{9}{10}}) - ln ((x + 3)^{\frac{12}{5}}) = ln (\frac{( 2 x + 4 ) ^{\frac{9}{10}}}{( x + 3 ) ^{\frac{12}{5}}})

= ln (\frac{( 2 x + 4 ) ^{\frac{9}{10}}}{( x + 3 ) ^{\frac{12}{5}}})

ln (- 0.21 + 6) - ln (2 (- 0.21) - 1)

ln (\frac{8.5}{5.1})

ln ((x - a)^{2} + a^{2}) - ln ((y - a)^{2} + a^{2})

\frac{1}{2} lo g_{5} (2)

ln (\frac{x}{400})

What is 9/10 ln(2x+4)-12/5 ln(x+3) ?
The solution to 9/10 ln(2x+4)-12/5 ln(x+3) is ln(((2x+4)^{9/10})/((x+3)^{12/5)})