What is ln(5x)+ln(2y^3)-ln(x^2y) ?

The solution to ln(5x)+ln(2y^3)-ln(x^2y) is ln((10y^2)/x)

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simplify ln(5x)+ln(2y^3)-ln(x^2y)

simplify

ln (5 x) + ln (2 y^{3}) - ln (x^{2} y)

ln (\frac{10 y ^{2}}{x})

Solution steps

ln (5 x) + ln (2 y^{3}) - ln (x^{2} y)

Apply log rule:

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

ln (5 x) + ln (2 y^{3}) = ln (5 \cdot 2 x y^{3})

= ln (5 \cdot 2 x y^{3}) - ln (x^{2} y)

Multiply the numbers:

5 \cdot 2 = 10

= ln (10 x y^{3}) - ln (x^{2} y)

Apply log rule:

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

ln (10 x y^{3}) - ln (x^{2} y) = ln (\frac{10 x y ^{3}}{x ^{2} y})

= ln (\frac{10 x y ^{3}}{x ^{2} y})

Simplify

\frac{10 x y ^{3}}{x ^{2} y} : \frac{10 y ^{2}}{x}

= ln (\frac{10 y ^{2}}{x})

3 lo g_{b} (x + 2) - lo g_{b} (x)

ln (\frac{1}{k})

ln (13) - ln (3)

\frac{1}{10} ln (\frac{550}{500})

- ln (\frac{1}{2}) + ln (1)

What is ln(5x)+ln(2y^3)-ln(x^2y) ?
The solution to ln(5x)+ln(2y^3)-ln(x^2y) is ln((10y^2)/x)