What is 2ln(a)+3ln(b)-4ln(c) ?

The solution to 2ln(a)+3ln(b)-4ln(c) is ln((a^2b^3)/(c^4))

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simplify 2ln(a)+3ln(b)-4ln(c)

simplify

2 ln (a) + 3 ln (b) - 4 ln (c)

ln (\frac{a ^{2} b ^{3}}{c ^{4}})

Solution steps

2 ln (a) + 3 ln (b) - 4 ln (c)

Apply log rule:

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

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

= ln (a^{2}) + 3 ln (b) - 4 ln (c)

Apply log rule:

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

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

= ln (a^{2}) + ln (b^{3}) - 4 ln (c)

Apply log rule:

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

ln (a^{2}) + ln (b^{3}) = ln (a^{2} b^{3})

= ln (a^{2} b^{3}) - 4 ln (c)

Apply log rule:

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

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

= ln (a^{2} b^{3}) - ln (c^{4})

Apply log rule:

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

ln (a^{2} b^{3}) - ln (c^{4}) = ln (\frac{a ^{2} b ^{3}}{c ^{4}})

= ln (\frac{a ^{2} b ^{3}}{c ^{4}})

\frac{ln ( 1.5 ) - ln ( 2 )}{1.5 - 2}

ln (x) + ln (7 - x)

2 ln (6) - 5 ln (z - 4)

- 2 ln (\frac{9}{10})

ln (\frac{x}{760})

What is 2ln(a)+3ln(b)-4ln(c) ?
The solution to 2ln(a)+3ln(b)-4ln(c) is ln((a^2b^3)/(c^4))