What is log_{1/2}((3x^2)/2) ?

The solution to log_{1/2}((3x^2)/2) is -log_{2}(3)-2log_{2}(x)+1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{1/2}((3x^2)/2)

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{\frac{1}{a}} (x) = - lo g_{a} (x)

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

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

Apply log rule:

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

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

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

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

lo g_{2} (2) = 1

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

Apply the distributive law:

- (a + b) = - a - b

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

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

lo g_{3} (x) + lo g_{3} (x + 9)

\frac{lo g _{10} ( a ) + lo g _{10} ( b )}{lo g _{10} ( a ) lo g _{10} ( b )}

lo g_{4} (5) + lo g_{4} (7)

3 lo g_{10} (m) - 2 lo g_{10} (n)

What is log_{1/2}((3x^2)/2) ?
The solution to log_{1/2}((3x^2)/2) is -log_{2}(3)-2log_{2}(x)+1