- #1
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Homework Statement
[itex]a^{log_{b}(c)}=c^{log_{b}(a)}[/itex]
The Attempt at a Solution
Take [itex]log_{a}[/itex] of both sides:
[itex]log_{a}(a^{log_{b}(c)})=log_{a}(c^{log_{b}(a)})[/itex]
gives:
[itex]log_{b}c=log_{b}alog_{a}c[/itex]
Looks like one more step for the RHS. I sort of see that the RHS should become [itex]log_{b}c[/itex] and then we'll be done. But standard log laws don't seem to help me make this step. Please help with this step/explain why this is so?