What is ln(((9x+16y))/((e^{(1))x^{(2)})}) ?

The solution to ln(((9x+16y))/((e^{(1))x^{(2)})}) is ln(9x+16y)-1-2ln(x)

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simplify ln(((9x+16y))/((e^{(1))x^{(2)})})

simplify

ln (\frac{( 9 x + 16 y )}{( e ^{(1)} x ^{(2)} )})

ln (9 x + 16 y) - 1 - 2 ln (x)

Solution steps

ln (\frac{( 9 x + 16 y )}{( e ^{(1)} x ^{(2)} )})

Apply log rule:

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

ln (\frac{( 9 x + 16 y )}{( e ^{(1)} x ^{(2)} )}) = ln ((9 x + 16 y)) - ln ((e^{(1)} x^{(2)}))

= ln (9 x + 16 y) - ln (e^{1} x^{2})

Apply log rule:

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

ln (e^{1} x^{2}) = ln (e^{1}) + ln (x^{2})

= ln (9 x + 16 y) - (ln (x^{2}) + ln (e^{1}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{1}) = 1 \cdot ln (e)

= ln (9 x + 16 y) - (1 \cdot ln (e) + ln (x^{2}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= ln (9 x + 16 y) - (1 \cdot ln (e) + 2 ln (x))

1 \cdot ln (e) = 1

= ln (9 x + 16 y) - (2 ln (x) + 1)

- (1 + 2 ln (x)) : - 1 - 2 ln (x)

= ln (9 x + 16 y) - 1 - 2 ln (x)

- lo g_{10} (6.9 \cdot 1 0^{- 10})

lo g_{3} (sin (x) cos (x)) - lo g_{3} (3^{x} e^{x})

\frac{1}{- ( 0.005 )} [0.8 ln (\frac{1}{8}) + 0.2 ln (\frac{9}{2})]

ln (e^{x} sin (2 x))

\frac{ln ( \frac{A}{b} )}{2 ln ( 10 )}

What is ln(((9x+16y))/((e^{(1))x^{(2)})}) ?
The solution to ln(((9x+16y))/((e^{(1))x^{(2)})}) is ln(9x+16y)-1-2ln(x)