What is simplify-log_{b}(1/4) ?

The solution to simplify-log_{b}(1/4) is 2log_{b}(2)

Popular >

simplify-log_{b}(1/4)

simplify

- lo g_{b} (\frac{1}{4})

2 lo g_{b} (2)

Solution steps

- lo g_{b} (\frac{1}{4})

\frac{1}{4} = 4^{- 1}

= - lo g_{b} (4^{- 1})

Apply log rule:

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

lo g_{b} (4^{- 1}) = - 1 \cdot lo g_{b} (4)

= - (- 1 \cdot lo g_{b} (4))

Apply rule:

1 \cdot a = a

- 1 \cdot lo g_{b} (4) = - lo g_{b} (4)

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

Factor the number:

4 = 2^{2}

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

Apply log rule:

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

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

= - (- 2 lo g_{b} (2))

Apply rule:

- (- a) = a

- (- 2 lo g_{b} (2)) = 2 lo g_{b} (2)

= 2 lo g_{b} (2)

lo g_{10} (12) - lo g_{10} (3)

lo g_{7} (\frac{7}{y})

ln (a + b) + ln (a - b) - 3 ln (c)

lo g_{3} (10 x) - lo g_{3} (2)

ln (2 x^{2})

What is simplify-log_{b}(1/4) ?
The solution to simplify-log_{b}(1/4) is 2log_{b}(2)