log base 5 of (8) * log base 64 of (25)
Could someone show me the steps so I can apply it to my other hw problems.
Thanks,
Mr_GREEN
Hello, Mr_Green!
Are you allowed to use the Base-Change Formula?
Simplify: .$\displaystyle \log_5(8)\cdot\log_{64}(25)$
Using the Base-Change Formula, we have: .$\displaystyle \frac{\log(8)}{\log(5)}\cdot\frac{\log(25)}{\log(6 4)}$
. . $\displaystyle = \:\frac{\log(8)}{\log(5)}\cdot\frac{\log(5^2)}{\lo g(8^2)} \:=\:\frac{\log(8)}{\log(5)}\cdot\frac{2\!\cdot\!\ log(5)}{2\!\cdot\!\log(8)} \:=\:1$