SOLUTION: "If 5 to the 21st power * 4 to the 11th power = 2 * 10 to the nth power, what is the value of n?" With a calculator, the answer is 21. However, I would appreciate knowing how t

Algebra ->  Exponents -> SOLUTION: "If 5 to the 21st power * 4 to the 11th power = 2 * 10 to the nth power, what is the value of n?" With a calculator, the answer is 21. However, I would appreciate knowing how t      Log On


   

Question 102760: "If 5 to the 21st power * 4 to the 11th power = 2 * 10 to the nth power, what is the value of n?"
With a calculator, the answer is 21. However, I would appreciate knowing how to solve this problem without a calculator. Thank you.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
"If 5 to the 21st power * 4 to the 11th power = 2 * 10 to the nth power, what is the value of n?"
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[5^21] = 2*10^n
10^n = [5^21 * 4^11]/2
Take the log of both sides to get:
n = 21log5 + 11log4 - log2
The answer I get is 22.073
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You would not want to calculate this without a calculator.
I think you may have made a mistake in your posting.
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Cheers,
Stan H.