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

The solution to 2ln(3)+2ln(6)+2ln(2)+2ln(3)+2ln(x) is ln(11664x^2)

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

simplify

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

ln (11664 x^{2})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

2 ln (6) = ln (6^{2})

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

Apply log rule:

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

ln (3^{2}) + ln (6^{2}) = ln (3^{2} \cdot 6^{2})

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

3^{2} \cdot 6^{2} = 324

= ln (324) + 2 ln (2) + 2 ln (3) + 2 ln (x)

Apply log rule:

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

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

= ln (324) + ln (2^{2}) + 2 ln (3) + 2 ln (x)

Apply log rule:

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

ln (324) + ln (2^{2}) = ln (2^{2} \cdot 324)

= ln (2^{2} \cdot 324) + 2 ln (3) + 2 ln (x)

324 \cdot 2^{2} = 1296

= ln (1296) + 2 ln (3) + 2 ln (x)

Apply log rule:

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

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

= ln (1296) + ln (3^{2}) + 2 ln (x)

Apply log rule:

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

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

= ln (1296) + ln (3^{2}) + ln (x^{2})

Apply log rule:

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

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

= ln (1296) + ln (3^{2} x^{2})

3^{2} = 9

= ln (1296) + ln (9 x^{2})

Apply log rule:

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

ln (1296) + ln (9 x^{2}) = ln (1296 \cdot 9 x^{2})

= ln (1296 \cdot 9 x^{2})

Multiply the numbers:

1296 \cdot 9 = 11664

= ln (11664 x^{2})

ln (\frac{( e ^{x} + e ^{- x} )}{2})

ln (\frac{3}{4}) \cdot \frac{3}{4} + ln (\frac{1}{4}) \cdot \frac{1}{4}

0.3 \cdot ln (x) - ln (x + 3)

- lo g_{10} (7.98 \cdot 1 0^{- 2})

ln (e^{x}) + ln (2)

What is 2ln(3)+2ln(6)+2ln(2)+2ln(3)+2ln(x) ?
The solution to 2ln(3)+2ln(6)+2ln(2)+2ln(3)+2ln(x) is ln(11664x^2)