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Popular >

simplify (log_{3}(7))(log_{7}(3))

Solution

simplify

(lo g_{3} (7)) (lo g_{7} (3))

Solution

1

Solution steps

(lo g_{3} (7)) (lo g_{7} (3))

(lo g_{3} (7)) (lo g_{7} (3)) = lo g_{3} (7) lo g_{7} (3)

= lo g_{3} (7) lo g_{7} (3)

Apply log rule:

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

lo g_{3} (7) = \frac{ln ( 7 )}{ln ( 3 )}

= \frac{ln ( 7 )}{ln ( 3 )} lo g_{7} (3)

Apply log rule:

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

lo g_{7} (3) = \frac{ln ( 3 )}{ln ( 7 )}

= \frac{ln ( 7 )}{ln ( 3 )} \cdot \frac{ln ( 3 )}{ln ( 7 )}

Cross cancel:

\frac{a}{b} \cdot \frac{b}{a} = 1

= 1

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Frequently Asked Questions (FAQ)

What is (log_{3}(7))(log_{7}(3)) ?
The solution to (log_{3}(7))(log_{7}(3)) is 1