What is simplify-log_{b}(1/8) ?

The solution to simplify-log_{b}(1/8) is 3log_{b}(2)

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simplify-log_{b}(1/8)

simplify

- lo g_{b} (\frac{1}{8})

3 lo g_{b} (2)

Solution steps

- lo g_{b} (\frac{1}{8})

\frac{1}{8} = 8^{- 1}

= - lo g_{b} (8^{- 1})

Apply log rule:

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

lo g_{b} (8^{- 1}) = - 1 \cdot lo g_{b} (8)

= - (- 1 \cdot lo g_{b} (8))

Apply rule:

1 \cdot a = a

- 1 \cdot lo g_{b} (8) = - lo g_{b} (8)

= - (- lo g_{b} (8))

Factor the number:

8 = 2^{3}

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

Apply log rule:

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

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

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

Apply rule:

- (- a) = a

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

= 3 lo g_{b} (2)

ln (x) + ln (x - 1)

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

2 lo g_{b} (6) - lo g_{b} (9)

\frac{1}{2} lo g_{10} (x) - 3 lo g_{10} (y) - lo g_{10} (z)

ln (\frac{81}{125})

What is simplify-log_{b}(1/8) ?
The solution to simplify-log_{b}(1/8) is 3log_{b}(2)