What is 3ln(a)+6ln(b)-ln(8) ?

The solution to 3ln(a)+6ln(b)-ln(8) is ln((a^3b^6)/8)

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simplify 3ln(a)+6ln(b)-ln(8)

simplify

3 ln (a) + 6 ln (b) - ln (8)

ln (\frac{a ^{3} b ^{6}}{8})

Solution steps

3 ln (a) + 6 ln (b) - ln (8)

Apply log rule:

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

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

= ln (a^{3}) + 6 ln (b) - ln (8)

Apply log rule:

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

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

= ln (a^{3}) + ln (b^{6}) - ln (8)

Apply log rule:

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

ln (a^{3}) + ln (b^{6}) = ln (a^{3} b^{6})

= ln (a^{3} b^{6}) - ln (8)

Apply log rule:

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

ln (a^{3} b^{6}) - ln (8) = ln (\frac{a ^{3} b ^{6}}{8})

= ln (\frac{a ^{3} b ^{6}}{8})

lo g_{10} (0^{'} 1)

lo g_{x} (\frac{a ^{3} b}{c})

- lo g_{10} (6.28 \cdot 1 0^{- 5})

lo g_{10} (4 x) - lo g_{10} (12 + x)

ln (\frac{x ^{2} - 7}{( x - 3 ) ^{4}})

What is 3ln(a)+6ln(b)-ln(8) ?
The solution to 3ln(a)+6ln(b)-ln(8) is ln((a^3b^6)/8)