SOLUTION: Solve for t algebraically. Round answers to the nearest hundredth. 100(1/2)^t/5 = 20 So,I know you divide the whole equation by 100,which leaves me with, (1/2)^t/5 = 1/5

Question 1106244: Solve for t algebraically. Round answers to the nearest hundredth.
100(1/2)^t/5 = 20
So,I know you divide the whole equation by 100,which leaves me with,
(1/2)^t/5 = 1/5
Then I take the log of each side, my book tells me to use ln, so I end up with
ln(1/2)^t/5 = ln 1/5
Move t/5 over, now I get
t/5 ln(1/2) = ln 1/5
Multiply everything by 5
t ln(1/2) = 5 ln 1/5
Is that correct? I've tried everything I can think of, yet I still get the wrong answer. Would you please help me?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Solve for t algebraically. Round answers to the nearest hundredth.
100(1/2)^t/5 = 20
So,I know you divide the whole equation by 100,which leaves me with,
(1/2)^t/5 = 1/5
Then I take the log of each side, my book tells me to use ln, so I end up with
ln((1/2)^t/5) = ln 1/5
Move t/5 over, now I get
t/5 ln(1/2) = ln(1/5)
======================
t/5 = ln(1/5)/ln(1/2)
Multiply everything by 5
t = 5ln(1/5)/ln(1/2)
Then use a calculator.
t =~ 11.61

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