What is log_{3}(4)*log_{8}(3) ?

The solution to log_{3}(4)*log_{8}(3) is 2/3

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simplify log_{3}(4)*log_{8}(3)

simplify

lo g_{3} (4) \cdot lo g_{8} (3)

\frac{2}{3}

Decimal Notation

0.66666 \dots

Solution steps

lo g_{3} (4) lo g_{8} (3)

Apply log rule:

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

lo g_{3} (4) = \frac{ln ( 4 )}{ln ( 3 )}

= \frac{ln ( 4 )}{ln ( 3 )} lo g_{8} (3)

Apply log rule:

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

lo g_{8} (3) = \frac{ln ( 3 )}{ln ( 8 )}

= \frac{ln ( 4 )}{ln ( 3 )} \cdot \frac{ln ( 3 )}{ln ( 8 )}

Cross-cancel common factor:

ln (3)

= \frac{ln ( 4 )}{ln ( 8 )}

ln (4) = 2 ln (2)

ln (8) = 3 ln (2)

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

Cancel the common factor:

ln (2)

= \frac{2}{3}

5 \frac{3}{4}

x^{3} - 2 x

12 \times 4

\frac{16}{6}

\frac{4}{14}