How do you solve (log_x (7)(log_7 (5)) = 6(logx(7)(log7(5))=6?

1 Answer
Bdub
Mar 3, 2016

(log7)/(logx)*(log5)/(log7)=6->log5/logx=6->log_x5=6->x^6=5->x=5^(1/6)=root6(5)log7logx⋅log5log7=6→log5logx=6→logx5=6→x6=5→x=516=6√5

Explanation:

Use change of base formulalog_bx=logb/logxlogbx=logblogx to rewrite each logarithm and then simplify then solve for x

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