What is ((log_{3}(106)-log_{3}(5)))/(log_{3)(8)} ?

The solution to ((log_{3}(106)-log_{3}(5)))/(log_{3)(8)} is log_{8}(106/5)

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simplify ((log_{3}(106)-log_{3}(5)))/(log_{3)(8)}

simplify

\frac{( lo g _{3} ( 106 ) - lo g _{3} ( 5 ) )}{lo g _{3} ( 8 )}

lo g_{8} (\frac{106}{5})

Decimal Notation

1.46866 \dots

Solution steps

\frac{lo g _{3} ( 106 ) - lo g _{3} ( 5 )}{lo g _{3} ( 8 )}

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{3} (106) - lo g_{3} (5) = lo g_{3} (\frac{106}{5})

= \frac{lo g _{3} ( \frac{106}{5} )}{lo g _{3} ( 8 )}

Apply log rule:

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

\frac{lo g _{3} ( \frac{106}{5} )}{lo g _{3} ( 8 )} = lo g_{8} (\frac{106}{5})

= lo g_{8} (\frac{106}{5})

ln (a) + ln (b) + ln (c)

lo g_{3} (4) + lo g_{3} (x) - lo g_{3} (5)

ln (\frac{3 d ^{2}}{4 ^{- 1}})

(\frac{1}{2}) ln (\frac{0.7}{0.3})

ln (2 x e^{x})

What is ((log_{3}(106)-log_{3}(5)))/(log_{3)(8)} ?
The solution to ((log_{3}(106)-log_{3}(5)))/(log_{3)(8)} is log_{8}(106/5)