What is changebase log_{9}(8) ?

The solution to changebase log_{9}(8) is (3ln(2))/(2ln(3))

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changebase log_{9}(8)

change base

lo g_{9} (8)

\frac{3 ln ( 2 )}{2 ln ( 3 )}

Decimal Notation

0.94639 \dots

Solution steps

lo g_{9} (8)

Apply log rule:

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

lo g_{9} (8) = \frac{ln ( 8 )}{ln ( 9 )}

= \frac{ln ( 8 )}{ln ( 9 )}

Simplify

ln (9) : 2 ln (3)

= \frac{ln ( 8 )}{2 ln ( 3 )}

Simplify

ln (8) : 3 ln (2)

= \frac{3 ln ( 2 )}{2 ln ( 3 )}

0.75 \cdot ln (10000) + 0.25 \cdot ln (9000)

0 - \frac{0.025693}{2} ln (\frac{3}{2.4 \cdot 1 0 ^{- 3}})

ln (\frac{x ^{2} cos ( x )}{1 + x})

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

\frac{3 ln ( 7 ) + 7 ln ( 2 )}{ln ( 7 ) - 2 ln ( 2 )} - 0

What is changebase log_{9}(8) ?
The solution to changebase log_{9}(8) is (3ln(2))/(2ln(3))