What is e^{(x-2y)}-ln(2x^{(2)}y) ?

The solution to e^{(x-2y)}-ln(2x^{(2)}y) is e^{x-2y}-ln(2)-2ln(x)-ln(y)

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simplify e^{(x-2y)}-ln(2x^{(2)}y)

simplify

e^{(x - 2 y)} - ln (2 x^{(2)} y)

e^{x - 2 y} - ln (2) - 2 ln (x) - ln (y)

Solution steps

e^{(x - 2 y)} - ln (2 x^{(2)} y)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

= e^{x - 2 y} - ln (2) - 2 ln (x) - ln (y)

lo g_{a} (\frac{( 5 ^{2} y )}{- 1 ^{3}})

ln (\frac{1}{0.975})

ln (\frac{0.23113}{4.98 \cdot 1 0 ^{- 3}})

x (ln (3 x - 1) - ln (3 x - 3))

\frac{1}{6} [5 ln (x + 5) - ln (x) - ln (x^{2} - 9)]

What is e^{(x-2y)}-ln(2x^{(2)}y) ?
The solution to e^{(x-2y)}-ln(2x^{(2)}y) is e^{x-2y}-ln(2)-2ln(x)-ln(y)