What is 2log_{3}(4)-(log_{3}(2)+log_{3}(5)) ?

The solution to 2log_{3}(4)-(log_{3}(2)+log_{3}(5)) is log_{3}(8/5)

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simplify 2log_{3}(4)-(log_{3}(2)+log_{3}(5))

simplify

2 lo g_{3} (4) - (lo g_{3} (2) + lo g_{3} (5))

lo g_{3} (\frac{8}{5})

Decimal Notation

0.42781 \dots

Solution steps

2 lo g_{3} (4) - (lo g_{3} (2) + lo g_{3} (5))

2 lo g_{3} (4) = 4 lo g_{3} (2)

lo g_{3} (2) + lo g_{3} (5) = lo g_{3} (10)

= 4 lo g_{3} (2) - lo g_{3} (10)

Apply log rule:

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

4 lo g_{3} (2) = lo g_{3} (2^{4})

= lo g_{3} (2^{4}) - lo g_{3} (10)

Apply log rule:

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

lo g_{3} (2^{4}) - lo g_{3} (10) = lo g_{3} (\frac{2 ^{4}}{10})

= lo g_{3} (\frac{2 ^{4}}{10})

Cancel

\frac{2 ^{4}}{10} : \frac{8}{5}

= lo g_{3} (\frac{8}{5})

x^{5} y^{3} - x^{4} y^{4}

\frac{2 π}{1.5}

d^{2} - 5 d + 6

\frac{1 - \frac{x}{y}}{\frac{x ^{2}}{y ^{2}} - 1}

\frac{1}{8} - \frac{1}{4}

What is 2log_{3}(4)-(log_{3}(2)+log_{3}(5)) ?
The solution to 2log_{3}(4)-(log_{3}(2)+log_{3}(5)) is log_{3}(8/5)