What is log_{3}((a^3*b^2)/(c^4)) ?

The solution to log_{3}((a^3*b^2)/(c^4)) is 3log_{3}(a)+2log_{3}(b)-4log_{3}(c)

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simplify log_{3}((a^3*b^2)/(c^4))

simplify

lo g_{3} (\frac{a ^{3} \cdot b ^{2}}{c ^{4}})

3 lo g_{3} (a) + 2 lo g_{3} (b) - 4 lo g_{3} (c)

Solution steps

lo g_{3} (\frac{a ^{3} b ^{2}}{c ^{4}})

Apply log rule:

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

lo g_{3} (\frac{a ^{3} b ^{2}}{c ^{4}}) = lo g_{3} (a^{3} b^{2}) - lo g_{3} (c^{4})

= lo g_{3} (a^{3} b^{2}) - lo g_{3} (c^{4})

lo g_{3} (a^{3} b^{2}) = 3 lo g_{3} (a) + 2 lo g_{3} (b)

lo g_{3} (c^{4}) = 4 lo g_{3} (c)

= 3 lo g_{3} (a) + 2 lo g_{3} (b) - 4 lo g_{3} (c)

1036.36 \cdot ln (\frac{576}{249.2})

lo g_{10} (a^{2} - b^{2}) - lo g_{10} (a + b)

2.338 - 1.4995 - 0.287 \cdot ln (\frac{675}{45})

6 lo g_{4} (x) - 3 lo g_{4} (y)

What is log_{3}((a^3*b^2)/(c^4)) ?
The solution to log_{3}((a^3*b^2)/(c^4)) is 3log_{3}(a)+2log_{3}(b)-4log_{3}(c)