2012 Math Destroyer Test #7 Question 13

[drill-and-fill]

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If a = log 7(subscript) b^7, then what is the value of 7^a?

The answer says when 7 is raised to the power log7b^7, the result is b^7.

Wth does that mean?🙁 Can someone PLEASE explain this to me?

 

[nnal]

I'm not sure if I'll explain this correctly but I'll try. So basically, pretend the question was log (base 10) 100=x. In this case, you would look at it as if it was, 10^x=100 in which case, x=2. Sometimes, looking at the variables is confusing. In your problem, a = log (base 7) b^7, the problem is 7^a=b^7. So I guess the answer would just be b^7. Is that the answer? You pretty much take the base, raise to whatever it equals and then set that equal to the number next to the log.