What is log_{0.3}(10)-log_{0.3}(3) ?

The solution to log_{0.3}(10)-log_{0.3}(3) is -1

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simplify log_{0.3}(10)-log_{0.3}(3)

simplify

lo g_{0.3} (10) - lo g_{0.3} (3)

- 1

Solution steps

lo g_{0.3} (10) - lo g_{0.3} (3)

Apply log rule:

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

lo g_{0.3} (10) - lo g_{0.3} (3) = lo g_{0.3} (\frac{10}{3})

= lo g_{0.3} (\frac{10}{3})

0.3 = (\frac{10}{3})^{- 1}

= lo g_{(\frac{10}{3})^{- 1}} (\frac{10}{3})

Apply log rule

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x),

assuming

a \geq 0

= \frac{1}{- 1} lo g_{\frac{10}{3}} (\frac{10}{3})

Apply log rule:

lo g_{a} (a) = 1

= \frac{1}{- 1}

Simplify

= - 1

\frac{3}{4} lo g_{10} (7 + 43)

ln (\frac{2863}{1.0 8 ^{8}})

ln (\frac{5.0872}{4.8872})

6 lo g_{4} (7 z + 1) + \frac{1}{2} lo g_{4} (z + 2)

ln (x) + ln (\frac{y}{x} + 1) + \frac{2}{\frac{y}{x} + 1}

What is log_{0.3}(10)-log_{0.3}(3) ?
The solution to log_{0.3}(10)-log_{0.3}(3) is -1