What is ln((y+10)^2sqrt(y-5)) ?

The solution to ln((y+10)^2sqrt(y-5)) is 2ln(y+10)+ln(sqrt(y-5))

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simplify ln((y+10)^2sqrt(y-5))

simplify

ln ((y + 10)^{2} y - 5)

2 ln (y + 10) + ln (y - 5)

Solution steps

ln ((y + 10)^{2} y - 5)

Apply log rule:

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

ln ((y + 10)^{2} y - 5) = ln ((y + 10)^{2}) + ln (y - 5)

= ln ((y + 10)^{2}) + ln (y - 5)

Apply log rule:

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

ln ((y + 10)^{2}) = 2 ln (y + 10)

= 2 ln (y + 10) + ln (y - 5)

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

ln (x + 6) - ln (x - 4)

ln (\frac{( 3 x - 8 ) ^{2}}{5 x + 1})

2 lo g_{\frac{16}{3}} (6)

lo g_{10} (5 \cdot 1 0^{- 2})

What is ln((y+10)^2sqrt(y-5)) ?
The solution to ln((y+10)^2sqrt(y-5)) is 2ln(y+10)+ln(sqrt(y-5))