What is 3log_{3}(5)-log_{3}(4) ?

The solution to 3log_{3}(5)-log_{3}(4) is log_{3}(125/4)

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simplify 3log_{3}(5)-log_{3}(4)

simplify

3 lo g_{3} (5) - lo g_{3} (4)

lo g_{3} (\frac{125}{4})

Decimal Notation

3.13306 \dots

Solution steps

3 lo g_{3} (5) - lo g_{3} (4)

Apply log rule:

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

3 lo g_{3} (5) = lo g_{3} (5^{3})

= lo g_{3} (5^{3}) - lo g_{3} (4)

Apply log rule:

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

lo g_{3} (5^{3}) - lo g_{3} (4) = lo g_{3} (\frac{5 ^{3}}{4})

= lo g_{3} (\frac{5 ^{3}}{4})

5^{3} = 125

= lo g_{3} (\frac{125}{4})

\frac{7}{5} ln^{\frac{5}{7}} (\frac{1}{2})

ln (e (x - 6))

- \frac{1}{4} lo g_{2} (\frac{1}{4}) + (- \frac{3}{4} lo g_{2} (\frac{3}{4}))

lo g_{x} (x^{3} y) - lo g_{x} (x y)

lo g_{2} (x + 7) + lo g_{2} (11 - x)

What is 3log_{3}(5)-log_{3}(4) ?
The solution to 3log_{3}(5)-log_{3}(4) is log_{3}(125/4)