What is log_{2}(6)*log_{6}(8) ?

The solution to log_{2}(6)*log_{6}(8) is 3

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simplify log_{2}(6)*log_{6}(8)

simplify

lo g_{2} (6) \cdot lo g_{6} (8)

3

Solution steps

lo g_{2} (6) lo g_{6} (8)

Apply log rule:

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

lo g_{2} (6) = \frac{ln ( 6 )}{ln ( 2 )}

= \frac{ln ( 6 )}{ln ( 2 )} lo g_{6} (8)

Apply log rule:

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

lo g_{6} (8) = \frac{ln ( 8 )}{ln ( 6 )}

= \frac{ln ( 6 )}{ln ( 2 )} \cdot \frac{ln ( 8 )}{ln ( 6 )}

Cross-cancel common factor:

ln (6)

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

ln (8) = 3 ln (2)

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

Cancel the common factor:

ln (2)

= 3

\frac{5}{10} \cdot \frac{4}{9}

r + (- 8) = 10

\frac{x}{- 5} + 11 < 15

7 + 6 (x - 1) < 17 + 6 (x + 1) and 5 x - 7 \leq 3

8 (3 a + 6) = 9 (2 a - 4)