What is ln_{3}(0.2)+ln_{3}(1215) ?

The solution to ln_{3}(0.2)+ln_{3}(1215) is 5ln_{3}(3)

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simplify ln_{3}(0.2)+ln_{3}(1215)

simplify

ln_{3} (0.2) + ln_{3} (1215)

5 ln_{3} (3)

Solution steps

ln_{3} (0.2) + ln_{3} (1215)

Apply log rule:

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

ln_{3} (0.2) + ln_{3} (1215) = ln_{3} (1215 \cdot 0.2)

= ln_{3} (1215 \cdot 0.2)

Multiply the numbers:

0.2 \cdot 1215 = 243

= ln_{3} (243)

Rewrite

243

in power-base form:

243 = 3^{5}

= ln_{3} (3^{5})

Apply log rule:

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

ln_{3} (3^{5}) = 5 ln_{3} (3)

= 5 ln_{3} (3)

lo g_{10} (1215 x^{0.84})

ln (x) - 3 ln (z) + 0.5 ln (y)

lo g_{10} (x^{5} y^{3} z)

lo g_{10} (\frac{x}{w})

ln (1 \cdot 1 0^{- 3})

What is ln_{3}(0.2)+ln_{3}(1215) ?
The solution to ln_{3}(0.2)+ln_{3}(1215) is 5ln_{3}(3)