What is 2ln(a)-5ln(b)+ln(c) ?

The solution to 2ln(a)-5ln(b)+ln(c) is ln((a^2c)/(b^5))

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simplify 2ln(a)-5ln(b)+ln(c)

simplify

2 ln (a) - 5 ln (b) + ln (c)

ln (\frac{a ^{2} c}{b ^{5}})

Solution steps

2 ln (a) - 5 ln (b) + ln (c)

Apply log rule:

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

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

= ln (a^{2}) - 5 ln (b) + ln (c)

Apply log rule:

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

5 ln (b) = ln (b^{5})

= ln (a^{2}) - ln (b^{5}) + ln (c)

Apply log rule:

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

ln (a^{2}) - ln (b^{5}) = ln (\frac{a ^{2}}{b ^{5}})

= ln (\frac{a ^{2}}{b ^{5}}) + ln (c)

Apply log rule:

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

ln (\frac{a ^{2}}{b ^{5}}) + ln (c) = ln (c \frac{a ^{2}}{b ^{5}})

= ln (c \frac{a ^{2}}{b ^{5}})

Multiply fractions:

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

= ln (\frac{a ^{2} c}{b ^{5}})

ln (10 e^{- x})

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

lo g_{10} (x^{5} z)

lo g_{2} (x^{3})

ln (x) - ln (x - 2)

What is 2ln(a)-5ln(b)+ln(c) ?
The solution to 2ln(a)-5ln(b)+ln(c) is ln((a^2c)/(b^5))