What is 3ln(x)+2ln(x)-6ln(y) ?

The solution to 3ln(x)+2ln(x)-6ln(y) is ln((x^5)/(y^6))

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simplify 3ln(x)+2ln(x)-6ln(y)

simplify

3 ln (x) + 2 ln (x) - 6 ln (y)

ln (\frac{x ^{5}}{y ^{6}})

Solution steps

3 ln (x) + 2 ln (x) - 6 ln (y)

Apply log rule:

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

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

= 3 ln (x) + ln (x^{2}) - 6 ln (y)

Apply log rule:

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

6 ln (y) = ln (y^{6})

= 3 ln (x) + ln (x^{2}) - ln (y^{6})

Apply log rule:

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

ln (x^{2}) - ln (y^{6}) = ln (\frac{x ^{2}}{y ^{6}})

= 3 ln (x) + ln (\frac{x ^{2}}{y ^{6}})

Apply log rule:

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

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

= ln (x^{3}) + ln (\frac{x ^{2}}{y ^{6}})

Apply log rule:

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

ln (x^{3}) + ln (\frac{x ^{2}}{y ^{6}}) = ln (\frac{x ^{2}}{y ^{6}} x^{3})

= ln (\frac{x ^{2}}{y ^{6}} x^{3})

Simplify

x^{3} \frac{x ^{2}}{y ^{6}} : \frac{x ^{5}}{y ^{6}}

= ln (\frac{x ^{5}}{y ^{6}})

ln (x^{3} y)

0.0259 \cdot ln (\frac{2.8 \cdot 1 0 ^{19}}{7 \cdot 1 0 ^{15}})

93 + 10 lo g_{10} (5) - 40 lo g_{10} (2)

2 [ln (x + 3) + ln (x) - ln (x^{2} - 1)]

lo g_{4} ((m^{2} n^{3})^{5})

What is 3ln(x)+2ln(x)-6ln(y) ?
The solution to 3ln(x)+2ln(x)-6ln(y) is ln((x^5)/(y^6))