What is simplify log_{36}(6)log_{6}(36) ?

The solution to simplify log_{36}(6)log_{6}(36) is 1

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Evaluate log base 36 of 6 log base 6 of 36

simplify

lo g_{36} (6) lo g_{6} (36)

1

Solution steps

lo g_{36} (6) lo g_{6} (36)

Apply log rule:

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

lo g_{36} (6) = \frac{ln ( 6 )}{ln ( 36 )}

= \frac{ln ( 6 )}{ln ( 36 )} lo g_{6} (36)

Apply log rule:

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

lo g_{6} (36) = \frac{ln ( 36 )}{ln ( 6 )}

= \frac{ln ( 6 )}{ln ( 36 )} \cdot \frac{ln ( 36 )}{ln ( 6 )}

Cross cancel:

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

= 1

lo g_{10} (16) - lo g_{10} (8)

x, lo g_{x} (8000) = 3

y, lo g_{4} (64) = y

lo g_{3} (7)

x, lo g_{10} (5 x) = 3

What is simplify log_{36}(6)log_{6}(36) ?
The solution to simplify log_{36}(6)log_{6}(36) is 1