What is log_{a}(18)*log_{3}(a) ?

The solution to log_{a}(18)*log_{3}(a) is log_{3}(18)

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simplify log_{a}(18)*log_{3}(a)

simplify

lo g_{a} (18) \cdot lo g_{3} (a)

lo g_{3} (18)

Decimal Notation

2.63092 \dots

Solution steps

lo g_{a} (18) lo g_{3} (a)

Apply log rule:

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

lo g_{a} (18) = \frac{ln ( 18 )}{ln ( a )}

= \frac{ln ( 18 )}{ln ( a )} lo g_{3} (a)

Apply log rule:

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

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

= \frac{ln ( 18 )}{ln ( a )} \cdot \frac{ln ( a )}{ln ( 3 )}

Cross-cancel common factor:

ln (a)

= \frac{ln ( 18 )}{ln ( 3 )}

Apply log rule:

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

\frac{ln ( 18 )}{ln ( 3 )} = lo g_{3} (18)

= lo g_{3} (18)

(x - 2) (x + 5) < 0

- 3 a + 10 a = - 35

- 3 x^{2} - 18 x - 35 = 0

19 x + 18 = - 19 x + 18

What is log_{a}(18)*log_{3}(a) ?
The solution to log_{a}(18)*log_{3}(a) is log_{3}(18)