What is 2(log_{3}(20)-log_{3}(4))+0.5log_{3}(4) ?

The solution to 2(log_{3}(20)-log_{3}(4))+0.5log_{3}(4) is log_{3}(50)

Popular >

simplify 2(log_{3}(20)-log_{3}(4))+0.5log_{3}(4)

simplify

2 (lo g_{3} (20) - lo g_{3} (4)) + 0.5 lo g_{3} (4)

lo g_{3} (50)

Decimal Notation

3.56087 \dots

Solution steps

2 (lo g_{3} (20) - lo g_{3} (4)) + 0.5 lo g_{3} (4)

lo g_{3} (20) - lo g_{3} (4) = lo g_{3} (5)

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

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

Apply log rule:

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

2 lo g_{3} (5) = lo g_{3} (5^{2})

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

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{3} (5^{2}) + lo g_{3} (2) = lo g_{3} (5^{2} \cdot 2)

= lo g_{3} (5^{2} \cdot 2)

5^{2} \cdot 2 = 50

= lo g_{3} (50)

lo g_{10} (\frac{x ^{8} y ^{8}}{z ^{20}})

lo g_{10} (x^{2} + 3 x - 40) - lo g_{10} (x^{2} - 64)

3 lo g_{a} (2 x + 1) - 2 lo g_{a} (2 x - 1)

5 lo g_{10} (x) + 6 lo g_{10} (y)

What is 2(log_{3}(20)-log_{3}(4))+0.5log_{3}(4) ?
The solution to 2(log_{3}(20)-log_{3}(4))+0.5log_{3}(4) is log_{3}(50)