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Popular >

simplify log_{a}(b)*log_{b}(a)

Solution

simplify

lo g_{a} (b) \cdot lo g_{b} (a)

Solution

1

Solution steps

lo g_{a} (b) lo g_{b} (a)

Apply log rule:

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

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{ln ( b )}{ln ( a )} lo g_{b} (a)

Apply log rule:

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

lo g_{b} (a) = \frac{ln ( a )}{ln ( b )}

= \frac{ln ( b )}{ln ( a )} \cdot \frac{ln ( a )}{ln ( b )}

Cross cancel:

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

= 1

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Frequently Asked Questions (FAQ)

What is log_{a}(b)*log_{b}(a) ?
The solution to log_{a}(b)*log_{b}(a) is 1