What is log_{2}(3)*log_{3}(4) ?

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

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simplify log_{2}(3)*log_{3}(4)

simplify

lo g_{2} (3) \cdot lo g_{3} (4)

2

Solution steps

lo g_{2} (3) lo g_{3} (4)

Apply log rule:

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

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

= \frac{ln ( 3 )}{ln ( 2 )} lo g_{3} (4)

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 ( 3 )}{ln ( 2 )} \cdot \frac{ln ( 4 )}{ln ( 3 )}

Cross-cancel common factor:

ln (3)

= \frac{ln ( 4 )}{ln ( 2 )}

ln (4) = 2 ln (2)

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

Cancel the common factor:

ln (2)

= 2

3 (2 y - 4) - y = 5

3 x - 2 < x^{2}

\frac{t}{9} + 2 (\frac{t}{18} + 4) = 10

\frac{1}{2} (x - 1)^{2} + 5 = 23

27 x^{3} - 64 y^{3}