What is log_{1/4}(1/160) ?

The solution to log_{1/4}(1/160) is log_{4}(160)

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simplify log_{1/4}(1/160)

simplify

lo g_{\frac{1}{4}} (\frac{1}{160})

lo g_{4} (160)

Decimal

3.66096 \dots

Solution steps

lo g_{\frac{1}{4}} (\frac{1}{160})

Apply log rule:

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

lo g_{\frac{1}{4}} (\frac{1}{160}) = lo g_{\frac{1}{4}} (1) - lo g_{\frac{1}{4}} (160)

= lo g_{\frac{1}{4}} (1) - lo g_{\frac{1}{4}} (160)

Apply log rule:

lo g_{a} (1) = 0

= 0 - lo g_{\frac{1}{4}} (160)

0 - lo g_{\frac{1}{4}} (160) = - lo g_{\frac{1}{4}} (160)

= - lo g_{\frac{1}{4}} (160)

Apply log rule:

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

= - (- lo g_{4} (160))

Apply rule

- (- a) = a

= lo g_{4} (160)

ln x + x^{2} + 25 + C - ln (5)

ln (\frac{( sin ( x ^{2} ) ) ^{'}}{( cos ( 2 x ) ) ^{'}})

- ln (10) + ln (5)

ln (\frac{3 x - 2 y}{2 x + 2 y})

- lo g_{10} (1.58 \cdot 1 0^{- 5})