What is ln(2^2)+ln(x^5)-ln((x+3)^{-1/2}) ?

The solution to ln(2^2)+ln(x^5)-ln((x+3)^{-1/2}) is ln(4x^5(x+3)^{1/2})

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simplify ln(2^2)+ln(x^5)-ln((x+3)^{-1/2})

simplify

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

ln (4 x^{5} (x + 3)^{\frac{1}{2}})

Solution steps

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

Apply log rule:

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

ln (2^{2}) + ln (x^{5}) = ln (2^{2} x^{5})

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

2^{2} = 4

= ln (4 x^{5}) - ln ((x + 3)^{- \frac{1}{2}})

Apply log rule:

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

ln (4 x^{5}) - ln ((x + 3)^{- \frac{1}{2}}) = ln (\frac{4 x ^{5}}{( x + 3 ) ^{- \frac{1}{2}}})

= ln (\frac{4 x ^{5}}{( x + 3 ) ^{- \frac{1}{2}}})

Simplify

\frac{4 x ^{5}}{( x + 3 ) ^{- \frac{1}{2}}} : 4 x^{5} (x + 3)^{\frac{1}{2}}

= ln (4 x^{5} (x + 3)^{\frac{1}{2}})

ln (\frac{1}{2} x^{0.5} y^{0.5})

- \frac{8}{13} \cdot lo g_{2} (\frac{8}{13}) - \frac{5}{13} \cdot lo g_{2} (\frac{5}{13})

2 ln (z) - ln (n - a) + ln (x - a)

- ln (\frac{3}{8}) - ln (\frac{8}{3})

lo g_{10} (\frac{x y}{\frac{x}{y}} x^{2} y)

What is ln(2^2)+ln(x^5)-ln((x+3)^{-1/2}) ?
The solution to ln(2^2)+ln(x^5)-ln((x+3)^{-1/2}) is ln(4x^5(x+3)^{1/2})