Log(a) x = c; log(b) x=d Find the general statement expressing log(ab)x in terms of c and d?

i put the bases of the logs in parentheses. Log base a of x equals c and log base b of x equals d. Find the general statement expressing log base ab of x in terms of C and D.





How can I get the log bases combined?

Log(a) x = c; log(b) x=d Find the general statement expressing log(ab)x in terms of c and d?
log(a) x = c


x = a^c


x^(1/c) = a





log(b) x=d


x = b^d


x^(1/d) = b





x^(1/c + 1/d) = ab


x = (ab)^{ 1 / [ (1/c) + (1/d) ] }


x = (ab)^[ cd / (c + d) ]


log(ab)(x) = cd / (c + d).

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