What is 3ln(2)+4ln(x)-ln(5)-2ln(y) ?

The solution to 3ln(2)+4ln(x)-ln(5)-2ln(y) is ln((8x^4)/(5y^2))

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simplify 3ln(2)+4ln(x)-ln(5)-2ln(y)

simplify

3 ln (2) + 4 ln (x) - ln (5) - 2 ln (y)

ln (\frac{8 x ^{4}}{5 y ^{2}})

Solution steps

3 ln (2) + 4 ln (x) - ln (5) - 2 ln (y)

Apply log rule:

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

3 ln (2) = ln (2^{3})

= ln (2^{3}) + 4 ln (x) - ln (5) - 2 ln (y)

Apply log rule:

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

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

= ln (2^{3}) + ln (x^{4}) - ln (5) - 2 ln (y)

Apply log rule:

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

ln (2^{3}) + ln (x^{4}) = ln (2^{3} x^{4})

= ln (2^{3} x^{4}) - ln (5) - 2 ln (y)

2^{3} = 8

= ln (8 x^{4}) - ln (5) - 2 ln (y)

Apply log rule:

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

ln (8 x^{4}) - ln (5) = ln (\frac{8 x ^{4}}{5})

= ln (\frac{8 x ^{4}}{5}) - 2 ln (y)

Apply log rule:

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

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

= ln (\frac{8 x ^{4}}{5}) - ln (y^{2})

Apply log rule:

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

ln (\frac{8 x ^{4}}{5}) - ln (y^{2}) = ln (\frac{\frac{8 x ^{4}}{5}}{y ^{2}})

= ln (\frac{\frac{8 x ^{4}}{5}}{y ^{2}})

Apply the fraction rule:

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

= ln (\frac{8 x ^{4}}{5 y ^{2}})

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

lo g_{4} (9) + lo g_{4} (6)

3 ln (x) + 4 ln (y) - 6 ln (z)

lo g_{6} (6 x)

ln (\frac{5}{13})

What is 3ln(2)+4ln(x)-ln(5)-2ln(y) ?
The solution to 3ln(2)+4ln(x)-ln(5)-2ln(y) is ln((8x^4)/(5y^2))