Can anyone please help me with these log problems?

Question

http://online.math.uh.edu/Math1310/ch5/s54/LawLog/List/images/List5.gif (you dont have to do the calculator part)

and

http://online.math.uh.edu/Math1310/ch5/s54/LawLog/List/images/List6.gif

THANKS. Please show the steps?

Answer 1

1.) log(6) 40
The change of base formula for log(x) y is log y / log x.
log 40 / log 6 = 1.602 / 0.778 = 2.059

2.) For these, remember that log (ab) = log a + log b.
a.) ln 42 = ln 3 * ln 2 * ln 7
b.) log 45 = 2 log 3 * log 5