Solve the inequality for x. (enter your answers using interval notation.) ln x < 0

ok. let's solve ln x <0

solve ln x = 0

raise e to both sides

e^lnx = e^0
x=1

so we make a number line:
we add this root and any place that ln is undefined. you can't take the ln of anything less than or equal to 0, so we also put 0.

-undefneg...
01

we test a number bigger than 1 and a number less than 1.

since e>1, we can use it, and ln e = ln(e^1)= 1 > 0

since 0<1/e < 1, we can use it, and ln(1/e) = ln(e^-1) = -1 < 0

so ln x < 0 when 0

now lets try e^x > 6.

solve e^x = 6.

take ln of both sides.

x = ln 6.

< 6>6...
ln 6
e^x is always defined so we test a number bigger than ln 6 and a number less than ln 6.

0 < ln 6, so we can use it and e^0 = 1 < 6.

ln 7 > ln 6, since ln is always increasing. so we can use ln7, and e^ln 7 = 7 > 6.

so e^x > 6 for x>ln 6 or (ln 6, infinity).

Hope it helps

Ithink you're supposed to multiply 12.50 which is how much he makes per hour and then multiply it by each number then add whats left togrther and there's your answer