What is 1/2 log_{2}(5)-2log_{2}(6) ?

The solution to 1/2 log_{2}(5)-2log_{2}(6) is log_{2}((sqrt(5))/9)-2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 1/2 log_{2}(5)-2log_{2}(6)

simplify

\frac{1}{2} lo g_{2} (5) - 2 lo g_{2} (6)

lo g_{2} (\frac{5}{9}) - 2

Decimal Notation

- 4.00896 \dots

Solution steps

\frac{1}{2} lo g_{2} (5) - 2 lo g_{2} (6)

2 lo g_{2} (6) = 2 + 2 lo g_{2} (3)

= \frac{1}{2} lo g_{2} (5) - (2 + 2 lo g_{2} (3))

Apply the distributive law:

- (a + b) = - a - b

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

= \frac{1}{2} lo g_{2} (5) - 2 - 2 lo g_{2} (3)

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

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

= lo g_{2} (5^{\frac{1}{2}}) - 2 - lo g_{2} (3^{2})

lo g_{2} (5^{\frac{1}{2}}) - lo g_{2} (3^{2}) = lo g_{2} (\frac{5 ^{\frac{1}{2}}}{9})

= lo g_{2} (\frac{5 ^{\frac{1}{2}}}{9}) - 2

Apply exponent rule:

a^{\frac{1}{2}} = a

5^{\frac{1}{2}} = 5

= lo g_{2} (\frac{5}{9}) - 2

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

lo g_{10} (y) + 4 lo g_{10} (z)

lo g_{10} (4 x) - lo g_{10} (x)

lo g_{10} (a) + lo g_{10} (b) + lo g_{10} (c)

lo g_{4} (\frac{16}{x + 4})

What is 1/2 log_{2}(5)-2log_{2}(6) ?
The solution to 1/2 log_{2}(5)-2log_{2}(6) is log_{2}((sqrt(5))/9)-2