What is 1/2*log_{5}(324)-log_{5}(2) ?

The solution to 1/2*log_{5}(324)-log_{5}(2) is 2log_{5}(3)

Popular >

simplify 1/2*log_{5}(324)-log_{5}(2)

simplify

\frac{1}{2} \cdot lo g_{5} (324) - lo g_{5} (2)

2 lo g_{5} (3)

Decimal Notation

1.36521 \dots

Solution steps

\frac{1}{2} lo g_{5} (324) - lo g_{5} (2)

\frac{1}{2} lo g_{5} (324) = lo g_{5} (18)

= lo g_{5} (18) - lo g_{5} (2)

Apply log rule:

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

lo g_{5} (18) - lo g_{5} (2) = lo g_{5} (\frac{18}{2})

= lo g_{5} (\frac{18}{2})

Divide the numbers:

\frac{18}{2} = 9

= lo g_{5} (9)

Factor the number:

9 = 3^{2}

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

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

= 2 lo g_{5} (3)

4 ln (2) + 2 ln (x)

- (\frac{3}{9}) lo g_{2} (\frac{3}{9}) - (\frac{6}{9}) lo g_{2} (\frac{6}{9})

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

5 lo g_{4} (x) + \frac{1}{4} lo g_{4} (y) - 2

What is 1/2*log_{5}(324)-log_{5}(2) ?
The solution to 1/2*log_{5}(324)-log_{5}(2) is 2log_{5}(3)