What is log_{3}(a)*log_{10}(3) ?

The solution to log_{3}(a)*log_{10}(3) is log_{10}(a)

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simplify log_{3}(a)*log_{10}(3)

simplify

lo g_{3} (a) \cdot lo g_{10} (3)

lo g_{10} (a)

Solution steps

lo g_{3} (a) lo g_{10} (3)

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 ( a )}{ln ( 3 )} lo g_{10} (3)

Apply log rule:

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

lo g_{10} (3) = \frac{ln ( 3 )}{ln ( 10 )}

= \frac{ln ( a )}{ln ( 3 )} \cdot \frac{ln ( 3 )}{ln ( 10 )}

Cross-cancel common factor:

ln (3)

= \frac{ln ( a )}{ln ( 10 )}

Apply log rule:

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

\frac{ln ( a )}{ln ( 10 )} = lo g_{10} (a)

= lo g_{10} (a)

(1 + 3 i)^{9}

(- 2 + 8 i) - (- 8 + 4 i)

\frac{2 x ^{3}}{2 x ^{2}}

\frac{9 - x ^{2}}{x - 3}

\frac{8}{5 - 6}

What is log_{3}(a)*log_{10}(3) ?
The solution to log_{3}(a)*log_{10}(3) is log_{10}(a)