+25 Let \(f(x) = \log_{3}(x)\)and \(g(x) = 3^x\).
What is the value of\(f(g(f(f(f(g(27))))))?\)
The solution of the equation \(7^{x+7} = 8^x\)can be expressed in the form \(x = \log_{b}\left(7^7\right).\)
What is \(b\)?
Solve for \(n\) given that \(\log_{64}\left(\dfrac 1 2\right) + \log_{64}(1) + \log_{64}(2) + \log_{64}(4) + \log_{64}(8) + \log_{64}(n) = 2.\)
+214 For the first one, we can make use of the fact that f and g are inverses, so we can cancel to get f(f(27))=f(3)=1.
For the second one, set
\(7^x\cdot7^7=8^x\)
\(7^7=\frac{8^x}{7^x}=\frac{8}{7}^x\)
\(log_\frac{8}{7}{7^7}=x\)
So b is \(\frac{8}{7}\).
For the third one, the expression is equal to
-1/6 + 0 + 1/6 + 1/3 + 1/2 + \(log_{64}{n}\)=2
\(log_{64}{n}=\frac{7}{6}\)
\(n=128\)
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