What is changebase log_{1/7}(3) ?

The solution to changebase log_{1/7}(3) is -(ln(3))/(ln(7))

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changebase log_{1/7}(3)

change base

lo g_{\frac{1}{7}} (3)

- \frac{ln ( 3 )}{ln ( 7 )}

Decimal Notation

- 0.56457 \dots

Solution steps

lo g_{\frac{1}{7}} (3)

Apply log rule:

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

lo g_{\frac{1}{7}} (3) = \frac{ln ( 3 )}{ln ( \frac{1}{7} )}

= \frac{ln ( 3 )}{ln ( \frac{1}{7} )}

Simplify

ln (\frac{1}{7}) : - ln (7)

= \frac{ln ( 3 )}{- ln ( 7 )}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{ln ( 3 )}{ln ( 7 )}

lo g_{10} (\frac{1300}{2895}) + lo g_{10} (0.965)

2 ln ∣ x ∣ - ln x^{2} + 1 + arctan (x) + \frac{1}{x ^{2} + 1}

ln (55)

ln (x) - 3 ln (y) - ln (4)

What is changebase log_{1/7}(3) ?
The solution to changebase log_{1/7}(3) is -(ln(3))/(ln(7))