How do you solve $Log_(5)x + log_(3)x = 1$ ?

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Answer 1 · 2016-06-27T19:07:39

$x = 3^{(log_e 5)/(log_e 15)}$

We know that

$log_a b = (log_eb)/(log_e a)$

Then

$Log_(5)x + log_(3)x = 1->(log_e x)/(log_e 5)+(log_e x)/(log_e 3)=1$

or

$log_e x= (log_e 5 cdot log_e 3)/(log_e 5 + log_e 3)$

or

$x = e^{(log_e 5 cdot log_e 3)/(log_e 5 + log_e 3)}$

$x = 3^{(log_e 5)/(log_e 15)}$

How do you solve Log_(5)x + log_(3)x = 1Log_(5)x + log_(3)x = 1?