What is simplify-6ln(2)+15/2-6(ln(3)-ln(2))+7/2 ?

The solution to simplify-6ln(2)+15/2-6(ln(3)-ln(2))+7/2 is -6ln(3)+11

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simplify-6ln(2)+15/2-6(ln(3)-ln(2))+7/2

simplify

- 6 ln (2) + \frac{15}{2} - 6 (ln (3) - ln (2)) + \frac{7}{2}

- 6 ln (3) + 11

Decimal Notation

4.40832 \dots

Solution steps

- 6 ln (2) + \frac{15}{2} - 6 (ln (3) - ln (2)) + \frac{7}{2}

Apply log rule:

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

ln (3) - ln (2) = ln (\frac{3}{2})

= - 6 ln (2) + \frac{15}{2} - 6 ln (\frac{3}{2}) + \frac{7}{2}

Apply log rule:

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

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

= - ln (2^{6}) + \frac{15}{2} - 6 ln (\frac{3}{2}) + \frac{7}{2}

Apply log rule:

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

6 ln (\frac{3}{2}) = ln ((\frac{3}{2})^{6})

= - ln (2^{6}) + \frac{15}{2} - ln ((\frac{3}{2})^{6}) + \frac{7}{2}

Rewrite

- ln (2^{6}) - ln ((\frac{3}{2})^{6})

- (ln (2^{6}) + ln ((\frac{3}{2})^{6}))

= - (ln (2^{6}) + ln ((\frac{3}{2})^{6})) + \frac{15}{2} + \frac{7}{2}

Apply log rule:

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

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

= - ln (2^{6} (\frac{3}{2})^{6}) + \frac{15}{2} + \frac{7}{2}

2^{6} (\frac{3}{2})^{6} = 729

= - ln (729) + \frac{15}{2} + \frac{7}{2}

Combine the fractions

\frac{15}{2} + \frac{7}{2} : 11

= - ln (729) + 11

ln (729) = 6 ln (3)

= - 6 ln (3) + 11

lo g_{4} (x^{2} - 11 x + 28) - lo g_{4} (x - 7)

- 3 lo g_{7} (x) + 5 lo g_{7} (y) - lo g_{3} (z)

14 + lo g_{10} (\frac{0.00084}{48})

ln (7 x^{2} - 1) - ln (x^{2})

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

What is simplify-6ln(2)+15/2-6(ln(3)-ln(2))+7/2 ?
The solution to simplify-6ln(2)+15/2-6(ln(3)-ln(2))+7/2 is -6ln(3)+11