What is 0.5log_{3}(6)-0.25log_{3}(4) ?

The solution to 0.5log_{3}(6)-0.25log_{3}(4) is 0.5

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simplify 0.5log_{3}(6)-0.25log_{3}(4)

simplify

0.5 lo g_{3} (6) - 0.25 lo g_{3} (4)

0.5

Solution steps

0.5 lo g_{3} (6) - 0.25 lo g_{3} (4)

0.5 lo g_{3} (6) = lo g_{3} (6^{0.5})

- 0.25 lo g_{3} (4) = - lo g_{3} (4^{0.25})

= lo g_{3} (6^{0.5}) - lo g_{3} (4^{0.25})

Apply log rule:

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

lo g_{3} (6^{0.5}) - lo g_{3} (4^{0.25}) = lo g_{3} (\frac{6 ^{0.5}}{4 ^{0.25}})

= lo g_{3} (\frac{6 ^{0.5}}{4 ^{0.25}})

Cancel

\frac{6 ^{0.5}}{4 ^{0.25}} : 3^{0.5}

= lo g_{3} (3^{0.5})

Apply log rule:

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

= 0.5

ln (2.46) - ln (17.39)

- lo g_{10} (6.18 \cdot 1 0^{- 6})

\frac{1}{3} ln (\frac{8}{5})

- lo g_{10} (2.02 \cdot 1 0^{- 2})

ln (6) - ln (15) + ln (20)

What is 0.5log_{3}(6)-0.25log_{3}(4) ?
The solution to 0.5log_{3}(6)-0.25log_{3}(4) is 0.5