What is 1/2 ln(4)-4ln(x)+ln(y+7) ?

The solution to 1/2 ln(4)-4ln(x)+ln(y+7) is ln((2(y+7))/(x^4))

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simplify 1/2 ln(4)-4ln(x)+ln(y+7)

simplify

\frac{1}{2} ln (4) - 4 ln (x) + ln (y + 7)

ln (\frac{2 ( y + 7 )}{x ^{4}})

Solution steps

\frac{1}{2} ln (4) - 4 ln (x) + ln (y + 7)

Apply log rule:

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

\frac{1}{2} ln (4) = ln (4^{\frac{1}{2}})

= ln (4^{\frac{1}{2}}) - 4 ln (x) + ln (y + 7)

Apply log rule:

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

4 ln (x) = ln (x^{4})

= ln (4^{\frac{1}{2}}) - ln (x^{4}) + ln (y + 7)

Apply log rule:

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

ln (4^{\frac{1}{2}}) - ln (x^{4}) = ln (\frac{4 ^{\frac{1}{2}}}{x ^{4}})

= ln (\frac{4 ^{\frac{1}{2}}}{x ^{4}}) + ln (y + 7)

4^{\frac{1}{2}} = 2

= ln (\frac{2}{x ^{4}}) + ln (y + 7)

Apply log rule:

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

ln (\frac{2}{x ^{4}}) + ln (y + 7) = ln (\frac{2}{x ^{4}} (y + 7))

= ln (\frac{2}{x ^{4}} (y + 7))

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= ln (\frac{2 ( y + 7 )}{x ^{4}})

lo g_{10} (x^{4} y)

- lo g_{10} (4.5 \times 1 0^{- 5})

3 lo g_{8} (y) + 2 lo g_{8} (y - 9)

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

lo g_{2} (a) + lo g_{2} (b) - 2 lo g_{2} (c)

What is 1/2 ln(4)-4ln(x)+ln(y+7) ?
The solution to 1/2 ln(4)-4ln(x)+ln(y+7) is ln((2(y+7))/(x^4))