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Popular >

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

Solution

simplify

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

Solution

- lo g_{2} (x) + 1

Solution steps

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

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

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

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

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

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

Apply log rule:

lo g_{a} (1) = 0

= 0 - lo g_{\frac{1}{2}} (2) + lo g_{\frac{1}{2}} (x)

0 - lo g_{\frac{1}{2}} (2) + lo g_{\frac{1}{2}} (x) = - lo g_{\frac{1}{2}} (2) + lo g_{\frac{1}{2}} (x)

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

Apply log rule:

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

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

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

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

Apply rule

- (- a) = a

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

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Frequently Asked Questions (FAQ)

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