How do you condense $3 ln 3 + ln 9$ $3 ln 3 + ln 9$ ?

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How do you condense $3 ln 3 + ln 9$ $3 ln 3 + ln 9$ ?

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Answer 1 · 2016-04-06T19:39:26

$ln 243$ $ln243$

Explanation:

$1$ $1$ . Start by using the natural logarithmic property, ${ln}_{b} (m^{n}) = n \cdot {ln}_{b} (m)$ $ln_color(purple)b(color(red)m^color(blue)n)=color(blue)n*ln_color(purple)b(color(red)m)$ , to simplify $3 ln 3$ $3ln3$ .

$3 ln 3 + ln 9$ $3ln3+ln9$

$= ln (3^{3}) + ln (9)$ $=ln(3^3)+ln(9)$

$2$ $2$ . Use the natural logarithmic property, ${ln}_{b} (m \cdot n) = {ln}_{b} (m) + {ln}_{b} (n)$ $ln_color(purple)b(color(red)m*color(blue)n)=ln_color(purple)b(color(red)m)+ln_color(purple)b(color(blue)n)$ , to simplify the expression.

$= ln (3^{3} \cdot 9)$ $=ln(3^3*9)$

$3$ $3$ . Simplify.

$= ln (27 \cdot 9)$ $=ln(27*9)$

$=color(green)(|bar(ul(color(white)(a/a)ln243color(white)(a/a)|)))$

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How do you condense $3 ln 3 + ln 9$ $3 ln 3 + ln 9$ ?

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