I am stuck on something that shouldn't be particularly complicated.
I have log_{x}(xlog_{y}y^{5})
Should I get 1+log_{x}5? This doesn't look right to me.
Instructions much appreciated.
Hello, Quixotic!
$\displaystyle \text{I have: }\:\log_x(x\log_yy^5)$
$\displaystyle \text{Should I get: }\:1+\log_x5\,?$ . Yes!
$\displaystyle \log_5(x\log_yy^5) \;=\;\log_5(x\cdot 5\log_yy) \qquad\quad \text{Note that: }\log_yy =1$
. . . . . . . . . . $\displaystyle =\;\log_5(x\cdot 5\cdot 1)$
. . . . . . . . . . $\displaystyle =\;\log_5(5x) $
. . . . . . . . . . $\displaystyle =\;\log_55 + \log_5x \qquad\quad\text{Note that: }\log_55 = 1$
. . . . . . . . . . $\displaystyle =\; 1 + \log_5x$