What is simplify-ln| 8/3+8/3 (0)|+ln| 2/3+8/3 (0)| ?

The solution to simplify-ln| 8/3+8/3 (0)|+ln| 2/3+8/3 (0)| is -2ln(2)

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simplify-ln| 8/3+8/3 (0)|+ln| 2/3+8/3 (0)|

simplify

- ln \frac{8}{3} + \frac{8}{3} (0) + ln \frac{2}{3} + \frac{8}{3} (0)

- 2 ln (2)

Decimal Notation

- 1.38629 \dots

Solution steps

- ln \frac{8}{3} + \frac{8}{3} (0) + ln \frac{2}{3} + \frac{8}{3} (0)

Apply log rule:

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

ln \frac{2}{3} + (0) \frac{8}{3} - ln \frac{8}{3} + (0) \frac{8}{3} = ln (\frac{0 \cdot \frac{8}{3} + \frac{2}{3}}{\frac{8}{3} + 0 \cdot \frac{8}{3}})

= ln (\frac{\frac{2}{3} + \frac{8}{3} \cdot 0}{\frac{8}{3} + \frac{8}{3} \cdot 0})

\frac{\frac{2}{3} + \frac{8}{3} ( 0 )}{\frac{8}{3} + \frac{8}{3} ( 0 )} = \frac{1}{4}

= ln (\frac{1}{4})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (4)

Rewrite

4

in power-base form:

4 = 2^{2}

= - ln (2^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= - 2 ln (2)

1 + 3 ln (x) - 4 ln (y) + \frac{1}{2} ln (z)

3 lo g_{10} (x) + lo g_{10} (2) - lo g_{10} (y)

lo g_{4} (\frac{f}{64})

lo g_{9} (x + 3) + lo g_{9} (4 x)

lo g_{2} (\frac{f}{8})

What is simplify-ln| 8/3+8/3 (0)|+ln| 2/3+8/3 (0)| ?
The solution to simplify-ln| 8/3+8/3 (0)|+ln| 2/3+8/3 (0)| is -2ln(2)