What is 5ln(a)+2ln(b)-7ln(c)+3ln(2) ?

The solution to 5ln(a)+2ln(b)-7ln(c)+3ln(2) is ln((8a^5b^2)/(c^7))

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simplify 5ln(a)+2ln(b)-7ln(c)+3ln(2)

simplify

5 ln (a) + 2 ln (b) - 7 ln (c) + 3 ln (2)

ln (\frac{8 a ^{5} b ^{2}}{c ^{7}})

Solution steps

5 ln (a) + 2 ln (b) - 7 ln (c) + 3 ln (2)

Apply log rule:

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

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

= ln (a^{5}) + 2 ln (b) - 7 ln (c) + 3 ln (2)

Apply log rule:

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

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

= ln (a^{5}) + ln (b^{2}) - 7 ln (c) + 3 ln (2)

Apply log rule:

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

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

= ln (a^{5} b^{2}) - 7 ln (c) + 3 ln (2)

Apply log rule:

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

7 ln (c) = ln (c^{7})

= ln (a^{5} b^{2}) - ln (c^{7}) + 3 ln (2)

Apply log rule:

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

ln (a^{5} b^{2}) - ln (c^{7}) = ln (\frac{a ^{5} b ^{2}}{c ^{7}})

= ln (\frac{a ^{5} b ^{2}}{c ^{7}}) + 3 ln (2)

Apply log rule:

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

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

= ln (\frac{a ^{5} b ^{2}}{c ^{7}}) + ln (2^{3})

Apply log rule:

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

ln (\frac{a ^{5} b ^{2}}{c ^{7}}) + ln (2^{3}) = ln (2^{3} \cdot \frac{a ^{5} b ^{2}}{c ^{7}})

= ln (2^{3} \cdot \frac{a ^{5} b ^{2}}{c ^{7}})

Simplify

\frac{a ^{5} b ^{2}}{c ^{7}} \cdot 2^{3} : \frac{8 a ^{5} b ^{2}}{c ^{7}}

= ln (\frac{8 a ^{5} b ^{2}}{c ^{7}})

4 lo g_{6} (x) + 8 lo g_{6} (y)

ln (x^{2} + 12 x + 11) - ln (x + 1)

lo g_{3} (\frac{9}{x + 6})

- \frac{ln ( \frac{9}{2} )}{3 ln ( 10 )}

10 \cdot lo g_{10} (\frac{2 \cdot 1 0 ^{- 3}}{1 0 ^{- 12}})

What is 5ln(a)+2ln(b)-7ln(c)+3ln(2) ?
The solution to 5ln(a)+2ln(b)-7ln(c)+3ln(2) is ln((8a^5b^2)/(c^7))